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%I A326235 #23 Aug 22 2021 13:30:36
%S A326235 52,74,137,159,238,242,304,306,456,478,547,701,756,988,1059,1186,1218,
%T A326235 1243,1378,1705,1976,2426,2596,2844,2952,3216,3263,3360,3632,3692,
%U A326235 3762,4094,4364,4603,4689,4858,5003,5177,5287,5361,5426,5999,6054,6285,6347,6417,6457,6639,6862,7269,7500
%N A326235 Numbers k such that N = (35k)^6 is a twin rank (A002822: 6N +- 1 are twin primes).
%C A326235 Dinculescu notes that if N = m^2 > 1 is a twin rank (i.e., in A002822), then m is a multiple of 5, and if N = m^3 > 1, then m is a multiple of 7, cf. A326231 and A326233. Thus, when N = m^6, then m is a multiple of 35, and here we list these m/35.
%C A326235 See A326236 for the numbers m.
%H A326235 A. Dinculescu and M. F. Hasler, <a href="/A326235/b326235.txt">Table of n, a(n) for n = 1..10000</a>
%H A326235 A. Dinculescu, <a href="http://www.utgjiu.ro/math/sma/v13/p13_11.pdf">On the Numbers that Determine the Distribution of Twin Primes</a>, Surveys in Mathematics and its Applications, 13 (2018), 171-181.
%F A326235 a(n) = A326236(n+1)/35.
%o A326235 (PARI) select( is(n)=!for(s=1,2,ispseudoprime(6*(35*n)^6+(-1)^s)||return), [1..10^4])
%Y A326235 Cf. A002822, A326231 (analog for m^2), A326232, A326233 (analog for m^3), A326234, A326236 ({1} U {35*a(n)}), A326230 (least twin rank m^n for given n).
%K A326235 nonn
%O A326235 1,1
%A A326235 _M. F. Hasler_ and _Antonie Dinculescu_, Jun 14 2019
%E A326235 a(1..10^4) independently computed using Mathematica and PARI/GP, by A. D. and _M. F. Hasler_, Jun 19 2019

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