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 2012-08-20, 16:23 #1 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 3×419 Posts OEIS missing sequences OEIS missing entries It would be good to include the following sequences into the OEIS. Unfortunately I do not have the access to it at all. 1. Mersenne Numbers, with all the prime factors of the form 1 (mod 3), which have a representation form a²+3b², for example the exponents 67, 101, 103 belong to this sequence, as such, but, on the other hand, the exponents 59, 71, 109, etc. do not at all It is being worthwhile to note that this type of sequence will contain no elements at all, for the a²+b² forms, a²+2b² forms since all Mersenne Numbers ≥ 7, are being for the form 7 (mod 8), so atleast one prime factor should be 7 (mod 8), being given away already Criteria for representation for a²+b² - all prime factors should be for form 1 (mod 4) Criteria for representation for a²+2b² - all prime factors should be for form 1 (mod 8) / 3 (mod 8) Criteria for representation for a²+3b² - all prime factors should be for form 1 (mod 3) 2. Rise away to extend with the all prime factors 1 (mod 3) forms, to the Fermat, Wagstaff, Repunits, other bases, as well as with the Fibonacci, Lucas, etc. cases if possible. For this example, consider with R19 = 360004294² + 3×571987185², etc. Ouch! a²+3b² forms is not being valid for the Fermat numbers at all, since they are being for the form 2 (mod 3), but a²+2b² forms seems to be valid for the Wagstaff numbers candidates for the form (2p+1)/3, as such 3. Base 2: 16, 24, 41, 220, 971, 972, 8554, 42485, 42486 A045875 smallest m for which 2^m contains n consecutive identical digits do so for the other bases extending into for these bases 3, 5, 6, 7, 11, etc. as well For example, for base 3, Forming away thereby, with this following sequence, thus this way away Base 3: 11, 32, 33, 274, 538, 2124, 7720, 22791, 107187, 107187 Base 5: 11, 50, 95, 125, 1087, 2786, 2790, 2796, 2797, 2802, 2803 Base 6: 5, 5, 115, 226, 371, 1503, 8533, 27717, 27717 Base 7: 6, 31, 71, 172, 175, 1961, 6176, 33836 Base 11: 1, 8, 39, 156, 482, 1323, 2983, 9443 etc. You could even include away some subsequences, for example, The least power of 3, with the some 9 consecutive digit N's, following away thereby this process 107189, 44152, 22791, 67449, 125406, 67390, 90785, 67448, 32311, 164065 4. A073733, A046104 Numerators, denominators for the continued fraction convergents for values for log 2. Do so for the other bases as well. They are being important, as such, as since they give away the power of N more closer enough increasingly to the power of 10. Do so them, that thing, for the other bases as well, which are being, namely log 3, log 5, log 6, log 7, log 11, etc. Get the help from http://wims.unice.fr/wims/wims.cgi?s...00&num_style=1 5. A028232 the continued fraction expansion for value for log 2, as such. Carry on over that same exploring thing away for the other bases as well. namely log 3, log 5, log 6, log 7, log 11, etc.
 2012-08-20, 18:30 #2 ewmayer ∂2ω=0     Sep 2002 República de California 2×32×653 Posts What do you you mean, you "do not have the access to [the OEIS] at all"? If you have internet access, you can submit to the OEIS. In the time it took you to compose your post, you could have done so.
 2012-08-20, 19:21 #3 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 100111010012 Posts I'm being afraid that I will have to request an account to register entry for the OEIS, similar to the Mersenne Wiki process, not direct account creation process at all. I do not have got the time right now to wait for an account, enter away, create an account for entering with few sequences alone, someone else can in fact do it. I have got some heavy duties to do so with, for few months, counting alone the processes following away with Furthermore, into entering a sequence into the OEIS, it - each sequence, everything has to await for an approval process. For this example, consider with A146556 Natural growth for an aliquot sequence driven by a perfect number driver 3, 5, 7, 9, 17, 19, 21, 43, 45, 111, 193, 195, 477, 927, 1777, 1779, 2973, 4963, 6397, 6399, 12961, 14983, 14985, 40191, 66993, 114063, 193233, 334959, 558273, 951999, 1586673, 3724815, 8255985 Does the OEIS have the same similar sequence starting from 11 onwards over going ontowards automatically the direction for oriented away purpose for the following sake process for the 11, 13, 15, 33, 63, 145, 215, 313, 315, 933, 1563, 2613, 5003, 5005, 11123, 14869, 14871, 24793, 24795, 68805, 193275, 499885, 770627, 1152637, 1152639, 2216961, 4187619, 9032861, 9092323, 9272573, 9414403, 9414405
2012-08-20, 19:32   #4
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

2×3×23×61 Posts

Quote:
 Originally Posted by ewmayer What do you you mean, you "do not have the access to [the OEIS] at all"? If you have internet access, you can submit to the OEIS. In the time it took you to compose your post, you could have done so.
Submit.html says this:

Quote:
 Since this is a scientific database, anonymous submissions cannot be accepted. You must request an account and log in before you can contribute a new sequence or edit an existing one. Your email address will be disguised before it appears in the entry, and we plan to remove email addresses entirely from public view as part of a future upgrade to the system.
I could Submit them if it's wanted, as can CRG, and a few other's I'd imagine.

Last fiddled with by science_man_88 on 2012-08-20 at 19:33

2012-08-20, 21:07   #5
ewmayer
2ω=0

Sep 2002
República de California

2×32×653 Posts

Quote:
 Originally Posted by Raman I'm too lazy.
Didn't even need Google Translate for that one.

2012-08-20, 23:57   #6
CRGreathouse

Aug 2006

598710 Posts

Quote:
 Originally Posted by Raman I'm being afraid that I will have to request an account to register entry for the OEIS, similar to the Mersenne Wiki process, not direct account creation process at all.
Accounts are approved daily by Neil and David. It's not a long process.

2012-08-21, 09:13   #7
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

3×419 Posts

Quote:
 Originally Posted by science_man_88 I could Submit them if it's wanted, as can CRG, and a few other's I'd imagine.
Could somebody please provide me with the list for
Mersenne Numbers, Repunits, Wagstaff (2p+1)/3 candidates, with no prime factor of the form 2 (mod 3) at all

if possible, then the Fibonacci, Lucas numbers, the other base tables, 10+ as well

Mersenne, Wagstaff, Fibonacci, Lucas till 1000
Repunits upto 300 to 400, if possibly, in case

The FactorDB does not seem to offer a function for filtering away with the lines, that which are being for the form 2 (mod 3)

The Fibonacci / Lucas numbers, to calculating away with its period is being a bit trickier, its order is being 8
following that thing with which, is it is being, away as follows, as since, as

Its irreducible polynomial (mod 3), is being
x²-x-1 = x²+2x+2 mod 3

x²-x-1 = 0 mod 3
1 → x → x+1 → 2x+1 → 2 → 2x → 2x+2 → x+2 → 1

In addition to that thing, the Wagstaff candidates, with the no prime factors for the form 5 (mod 8) / 7 (mod 8), can it to be easily for represented into the form a²+2b², it would be nice enough, to for the thing, it to be added to it

Last fiddled with by Raman on 2012-08-21 at 09:51

 2012-08-21, 09:59 #8 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 3·5·683 Posts List of Mersenne Numbers? 2^1-1=1 2^2-1=3 2^3-1=7 2^4-1=15 2^5-1=31 2^6-1=63 2^7-1=127 2^8-1=255 etc List of Mersenne Numbers with no factor 2 mod 3? (their exponents in first column, their factors in the second, no powers) Code: (16:54:17) gp > for(i=2,100,a=factorint(2^i-1)~; has=0; for(j=1,#a,if(a[1,j]%3==2,has=1;break)); if(has==0,print(i" -\t"a[1,]))) 2 - [3] 3 - [7] 5 - [31] 6 - [3, 7] 7 - [127] 9 - [7, 73] 13 - [8191] 14 - [3, 43, 127] 15 - [7, 31, 151] 17 - [131071] 18 - [3, 7, 19, 73] 19 - [524287] 21 - [7, 127, 337] 25 - [31, 601, 1801] 26 - [3, 2731, 8191] 27 - [7, 73, 262657] 31 - [2147483647] 37 - [223, 616318177] 38 - [3, 174763, 524287] 39 - [7, 79, 8191, 121369] 42 - [3, 7, 43, 127, 337, 5419] 45 - [7, 31, 73, 151, 631, 23311] 49 - [127, 4432676798593] 51 - [7, 103, 2143, 11119, 131071] 54 - [3, 7, 19, 73, 87211, 262657] 57 - [7, 32377, 524287, 1212847] 61 - [2305843009213693951] 62 - [3, 715827883, 2147483647] 63 - [7, 73, 127, 337, 92737, 649657] 65 - [31, 8191, 145295143558111] 67 - [193707721, 761838257287] 74 - [3, 223, 1777, 25781083, 616318177] 75 - [7, 31, 151, 601, 1801, 100801, 10567201] 78 - [3, 7, 79, 2731, 8191, 121369, 22366891] 81 - [7, 73, 2593, 71119, 262657, 97685839] 85 - [31, 131071, 9520972806333758431] 89 - [618970019642690137449562111] 93 - [7, 2147483647, 658812288653553079] 98 - [3, 43, 127, 4363953127297, 4432676798593] (16:54:36) gp > etc. Why do you need them for?
2012-08-21, 10:11   #9
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

23518 Posts

Thanks

Quote:
 Originally Posted by LaurV Why do you need them for?
Read away the first post for these things

Quote:
 Originally Posted by Raman OEIS missing entries It would be good to include the following sequences into the OEIS. 1. Mersenne Numbers, with all the prime factors of the form 1 (mod 3), which have a representation form a²+3b², for example the exponents 67, 101, 103 belong to this sequence, as such, but, on the other hand, the exponents 59, 71, 109, etc. do not at all
But thereby is it there some way being available, in order to store away the larger factors, for example for the numbers M727 etc., easily into the PARI/GP compiler script automatically

Last fiddled with by Raman on 2012-08-21 at 10:25

2012-08-21, 10:27   #10
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

3×5×683 Posts

Quote:
 Originally Posted by Raman Read the first post
I knew that post. My question was related to that guy called Guy who said that the number of small numbers is finite, but the number of properties we want to assign to those numbers is infinite... I can find few (whatever) properties by myself, check which numbers verify them, and make another OEIS entry. Who cares? What is that useful for?

2012-08-21, 10:53   #11
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

3×419 Posts

Quote:
 Originally Posted by LaurV What is that useful for?

If you ask for the use for inserting with my own sequence, then

What is A045875 being useful for? What for A146556?

What for the squares, cubes, powers, Fibonacci, Lucas, triangular numbers, pascal triangle, partition number, the collatz 27 thing, etc. thereby given away, 2*3^n, 3*2^n, 5*2^n, 7*2^n, 9*2^n, etc. sequences being useful for. I can calculate them by using my own hands. What for the A000001 the number of groups for given order?

Period.

This Mersenne numbers with no prime factors for the form 2 mod 3 at all would be alone another fancier sequence, being specialized away, thereby, but there exist specialized sequences into the OEIS alone for the sum of two squares, sum of two cubes, a²+2b² forms, a²+3b² forms, etc.

a²+3b² forms would be alone be useful for a suitable primality test, by taking away using its square root processes alone, as well as a suitable candidate for a future factorization method, number, if in case we can get two different representations for the a2+3b2 forms alone

Last fiddled with by Raman on 2012-08-21 at 10:57

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