This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173560 #18 Jul 19 2025 10:12:33
%S A173560 16,44,84,135,161,631,849,880,1035,1086,1721,1815,2155,2704,2871,2975,
%T A173560 3011,3159,3220,3365,3390,3669,3996,4075,4704,4761,5025,5090,5299,
%U A173560 5585,5640,5970,6314,6606,7035,7785,8104,8129,8610,9116,9665,9966,10249
%N A173560 Numbers m such that (6*m)^5 is a sum of a twin prime pair.
%C A173560 The twin prime pairs are characterized in A173255.
%C A173560 No such m has least significant digit (LSD) e = 2 or 7 because a = (6 * e)^5/2 - 1, representing the smaller of the twin primes, would get LSD 5.
%C A173560 No such m has LSD e = 3 or 8, because a+2 = (6 * e)^5/2 + 1, representing the larger prime, would get LSD 5.
%C A173560 The primes in this sequence here are a(6) = 631 = prime(115), a(11) = 1721 = prime(268),
%C A173560 a(17) = 3011 = prime(432), a(49) = 10859 = prime(1320), ...
%H A173560 Amiram Eldar, <a href="/A173560/b173560.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%e A173560 p = (6 * 16)^5/2 - 1 = 4076863487 = A000040(193435931); p+2 = A000040(193435932), so a(1) = 16.
%e A173560 p = (6 * 44)^5/2 - 1 = 641194278911 = A000040(24524572848); p+2 = A000040(24524572849), so a(2) = 44.
%e A173560 p = (6 * 84)^5/2 - 1 = 16260080320511 = A000040(553382827197); p+2 = A000040(553382827198), so a(3) = 84.
%t A173560 Select[Range[700],AllTrue[((6*#)^5-2)/2+{0,2},PrimeQ]&] (* _Harvey P. Dale_, Dec 21 2024 *)
%o A173560 (PARI) isok(m) = {my(k = (6*m)^5/2); isprime(k-1) && isprime(k+1);} \\ _Amiram Eldar_, Jul 19 2025
%Y A173560 Cf. A001359, A061308, A069496, A172271, A172494, A173255.
%K A173560 nonn
%O A173560 1,1
%A A173560 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 21 2010