Near RepSequence Primes - Page 2

Batalov · 2012-10-12, 20:59

Well, I thought - they stay near. They are all a subsequence of an infinite (123456789)_repeated

davar55 · 2012-10-13, 00:26

Yes, that's cool, a superset extension.

But k can be any integer, so I wrongly thought you missed that.
My bad.

Batalov · 2012-10-13, 01:00

I saw that. I just wanted to play with "rainbow" numbers first.

davar55 · 2012-10-13, 13:57

Just a suggestion: use k = a Mersenne prime exponent.

I don't mind seeing those digits repeating dizzyingly,
they're so familiar.

science_man_88 · 2012-10-13, 14:18

Quote:

Originally Posted by davar55

Just a suggestion: use k = a Mersenne prime exponent.

I don't mind seeing those digits repeating dizzyingly,
they're so familiar.

Code:

 a=[];for(k=1,#MeVec,for(n=0,20,for(d=0,9,if(isprime(MeVec[k] * (10^n*length(MeVec[k])-1) / (10^length(MeVec[k])-1) * 10 + d),a=concat(a,MeVec[k] * (10^n*length(MeVec[k])-1) / (>
a=[];for(k=1,#MeVec,for(n=0,20,for(d=0,9,if(isprime(MeVec[k]*(10^n*length(MeVec[k])-1)/(10^length(MeVec[k])-1)*10+d),a=concat(a,MeVec[k]*(10^n*length(MeVec[k])-1)/(10^length(MeVec[k])-1)*10+d)))));a=vecsort(a,,8)

in the results
I found:

Quote:

191, 193, 197, 199

Quote:

1871, 1873, 1877, 1879

davar55 · 2012-10-13, 14:54

Quote:

Originally Posted by science_man_88

Code:

 a=[];for(k=1,#MeVec,for(n=0,20,for(d=0,9,if(isprime(MeVec[k] * (10^n*length(MeVec[k])-1) / (10^length(MeVec[k])-1) * 10 + d),a=concat(a,MeVec[k] * (10^n*length(MeVec[k])-1) / (>
a=[];for(k=1,#MeVec,for(n=0,20,for(d=0,9,if(isprime(MeVec[k]*(10^n*length(MeVec[k])-1)/(10^length(MeVec[k])-1)*10+d),a=concat(a,MeVec[k]*(10^n*length(MeVec[k])-1)/(10^length(MeVec[k])-1)*10+d)))));a=vecsort(a,,8)

in the results
I found:

Those are fine, but if you find a 2- or 3- constellation with n >= 2
(so that the k sequence is repeated) that would be more interesting.

LaurV · 2012-10-13, 16:08

@sm88: those original formulas were missing a couple of parenthesis to be really repetitive sequences. They (the parenthesis) are "understandable" by humans, but for your pari you have to put them in.

davar55 · 2012-11-28, 20:37

Quote:

Originally Posted by Batalov

I saw that. I just wanted to play with "rainbow" numbers first.

I should have mentioned, nice label.
Mine was a bit cumbersome.

davar55 · 2015-01-02, 11:36

Near repsequence primes, near repdigit primes.
Potato potahto.

Batalov · 2015-01-02, 16:33

Your number doesn't have '0's, this one 'doesn't have '8's, but visually similar and much larger.
This is because the (64·10^n-1)/81 is much easier to sieve and test (small k and |c|=1, and lastly, algebraic eliminations!)

davar55 · 2015-01-02, 17:44

Quote:

Originally Posted by Batalov

Your number doesn't have '0's, this one 'doesn't have '8's, but visually similar and much larger.
This is because the (64·10^n-1)/81 is much easier to sieve and test (small k and |c|=1, and lastly, algebraic eliminations!)

Yes, I said I liked your name "rainbow" for these numbers that look like
a repeated spectrum of digits in sequence.

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2012-10-12, 20:59	#12
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9477₁₀ Posts	Well, I thought - they stay near. They are all a subsequence of an infinite (123456789)_repeated

2012-10-13, 00:26	#13
davar55 May 2004 New York City 2×29×73 Posts	Yes, that's cool, a superset extension. But k can be any integer, so I wrongly thought you missed that. My bad.

2012-10-13, 01:00	#14
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	I saw that. I just wanted to play with "rainbow" numbers first.

2012-10-13, 13:57	#15
davar55 May 2004 New York City 2·29·73 Posts	Just a suggestion: use k = a Mersenne prime exponent. I don't mind seeing those digits repeating dizzyingly, they're so familiar.

2012-10-13, 16:08	#18
LaurV Romulan Interpreter Jun 2011 Thailand 7×1,373 Posts	@sm88: those original formulas were missing a couple of parenthesis to be really repetitive sequences. They (the parenthesis) are "understandable" by humans, but for your pari you have to put them in.

2015-01-02, 11:36	#20
davar55 May 2004 New York City 2×29×73 Posts	Near repsequence primes, near repdigit primes. Potato potahto.

2015-01-02, 16:33	#21
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	Your number doesn't have '0's, this one 'doesn't have '8's, but visually similar and much larger. This is because the (64·10^n-1)/81 is much easier to sieve and test (small k and \|c\|=1, and lastly, algebraic eliminations!)