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 Showing results 1 to 25 of 1000 Search took 0.21 seconds. Search: Posts Made By: sweety439
 Forum: Riesel Prime Search 2021-09-15, 07:15 Replies: 267 Views: 46,637 Posted By sweety439 https://primes.utm.edu/primes/status.php id... https://primes.utm.edu/primes/status.php id 132704 and 132705 are palindromes.
 Forum: sweety439 2021-09-11, 03:24 Replies: 387 Views: 26,135 Posted By sweety439 Reference: Mersenne-Fermat primes... Reference: Mersenne-Fermat primes (https://archive.ph/20120529014233/http://staff.spd.dcu.ie/johnbcos/fermat6.htm), we can also consider generalized Mersenne-Fermat primes base b, the generalized...
 Forum: sweety439 2021-09-11, 03:18 Replies: 387 Views: 26,135 Posted By sweety439 List of generalized Saouter primes (i.e. primes... List of generalized Saouter primes (i.e. primes of the form (b^(2*3^n)+b^(3^n)+1)/gcd(b-1,3)) in bases 2<=b<=1024 Compare: List of generalized Fermat primes (i.e. primes of the form...
 Forum: sweety439 2021-09-10, 05:37 Replies: 177 Views: 17,131 Posted By sweety439 Newest data (minimal primes (start with b+1) up... Newest data (minimal primes (start with b+1) up to certain limit) for bases b=17 and b=18
 Forum: Aliquot Sequences 2021-09-10, 05:28 Replies: 11 Views: 752 Posted By sweety439 All strong infinity-touchable numbers are... All strong infinity-touchable numbers are infinity-touchable, since for all nonnegative integers n, there are only finitely many positive integers m such that s(m)=n (and the largest such m is at...
 Forum: Factoring 2021-09-10, 00:33 Replies: 427 Views: 73,770 Posted By sweety439 For HP(4), the smallest unsolved base is 13: ... For HP(4), the smallest unsolved base is 13: 2,31 3,67 4,37 5,457 6,79 7,368543395659524076221303587 8,14029
 Forum: Factoring 2021-09-09, 23:43 Replies: 427 Views: 73,770 Posted By sweety439 Here is the PARI/GP code, can calculate home... Here is the PARI/GP code, can calculate home prime for all bases b>=2, just type "home(n,b)" to find the home prime for integer n in base b step(n,b)=my(f=factor(n), v=[]); for(i=1, #f~,...
 Forum: Aliquot Sequences 2021-09-09, 02:48 Replies: 11 Views: 752 Posted By sweety439 We define "strong infinity-touchable number" as... We define "strong infinity-touchable number" as nonnegative integer n such that there exist infinitely many nonnegative integers whose Aliquot sequences reach n e.g. all nonnegative integers <52...
 Forum: Aliquot Sequences 2021-09-09, 02:47 Replies: 100 Views: 3,872 Posted By sweety439 There are amicable pairs which cannot be reached... There are amicable pairs which cannot be reached by any aliquot sequence starting from a number that does not belong to this pair, they are listed in the OEIS sequence A238382...
 Forum: sweety439 2021-09-08, 05:55 Replies: 177 Views: 17,131 Posted By sweety439 Some unsolved families are obvious through data... Some unsolved families are obvious through data for minimal primes (start with b+1) base b up to certain limit (https://en.wikiversity.org/wiki/Quasi-minimal_prime) Example 1: 80555551 is minimal...
 Forum: sweety439 2021-09-05, 20:35 Replies: 177 Views: 17,131 Posted By sweety439 Known unsolved families in bases b=17 and b=18: ... Known unsolved families in bases b=17 and b=18: b=17: F1{9} 1{7} 15{0}D 1F{0}7 51{0}D
 Forum: sweety439 2021-09-05, 20:31 Replies: 177 Views: 17,131 Posted By sweety439 Known minimal primes (start with b+1) in base... Known minimal primes (start with b+1) in base b=18: Small ones: (written in base b) 11, 15, 1B, 1D, 21, 25, 27, 2B, 2H, 35, 37, 3D, 3H, 41, 47, 4B, 4H, 57, 5B, 5D, 5H, 61, 65, 71, 75, 7B, 7D,...
 Forum: sweety439 2021-09-05, 20:27 Replies: 177 Views: 17,131 Posted By sweety439 Found by the smallest prime of the form xy{0}z or... Found by the smallest prime of the form xy{0}z or x{0}yz which no possible prime subsequence (i.e. no possible prime of the form x{0}y, x{0}z, y{0}z): (written in base 10) 17: 11{0}1: 307 17:...
 Forum: sweety439 2021-09-05, 20:23 Replies: 177 Views: 17,131 Posted By sweety439 Found by smallest generalized near-repdigit... Found by smallest generalized near-repdigit primes (i.e. of the form x{y} or {x}y) base b: (written in base 10) (the numbers whose repeating digit (i.e. y for x{y}, or x for {x}y) is 1 are not...
 Forum: sweety439 2021-09-05, 20:21 Replies: 177 Views: 17,131 Posted By sweety439 Known minimal primes (start with b+1) in base... Known minimal primes (start with b+1) in base b=17: Small ones: (written in base b) 12, 16, 1C, 1E, 23, 27, 29, 2D, 32, 38, 3A, 3G, 43, 45, 4B, 4F, 54, 5C, 5G, 61, 65, 67, 6B, 78, 7C, 81, 83,...
 Forum: Aliquot Sequences 2021-09-04, 14:33 Replies: 11 Views: 752 Posted By sweety439 No, there are three n such that s(n) = 284: 220,... No, there are three n such that s(n) = 284: 220, 562, 80089=283^2, and if the stronger version of Goldbach conjecture is true, then there are infinitely many numbers whose Aliquot sequence reach the...
 Forum: MattcAnderson 2021-09-04, 14:22 Replies: 6 Views: 423 Posted By sweety439 What is the natural density... What is the natural density (https://en.wikipedia.org/wiki/Natural_density) of A056561 (https://oeis.org/A056561)? Is it zero? Or positive?
 Forum: sweety439 2021-09-03, 23:36 Replies: 1,247 Views: 79,321 Posted By sweety439 Word files attached. Word files attached.
 Forum: sweety439 2021-09-03, 23:28 Replies: 1,247 Views: 79,321 Posted By sweety439 Status for 2<=b<=128 and 1<=k<=128: ... Status for 2<=b<=128 and 1<=k<=128: Sierpinski (k*b^n+1)/gcd(k+1,b-1)...
 Forum: sweety439 2021-09-03, 23:23 Replies: 1,247 Views: 79,321 Posted By sweety439 Status files: Sierpinski problems in bases... Status files: Sierpinski problems in bases b<=128 and b = 256, 512, 1024...
 Forum: sweety439 2021-09-03, 22:48 Replies: 7 Views: 121 Posted By sweety439 sequence A128033 4,3 5,13 7,3 8,3 ... sequence A128033 4,3 5,13 7,3 8,3 10,3 11,3 13,7
 Forum: sweety439 2021-09-03, 21:18 Replies: 7 Views: 121 Posted By sweety439 sequence A125958 (a,b) = (2*n-1,-2) can be... sequence A125958 (a,b) = (2*n-1,-2) can be extended to 2*n-1 = 231 (n = 116) 3,3 5,3 7,5 9,3 11,3 13,7 15,3
 Forum: sweety439 2021-09-03, 21:12 Replies: 7 Views: 121 Posted By sweety439 Thus the primitive part of the n-th term is... Thus the primitive part of the n-th term is Phi(n,a,b) = b^eulerphi(n) * Phi(n,(a/b)) Numbers n such that Phi(n,a,b) is prime for fixed a, b: ...
 Forum: sweety439 2021-09-03, 20:47 Replies: 7 Views: 121 Posted By sweety439 sequence A125954 (a,b) = (2*n+1,2) can be... sequence A125954 (a,b) = (2*n+1,2) can be extended to 2*n+1 = 183 (n = 91) 3,3 5,5 7,3 9,3 11,5 13,3 15,5
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