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%I #17 Jun 19 2019 17:15:29
%S 1,2,7,12,14,15,42,48,77,86,89,99,118,131,146,161,163,167,201,208,209,
%T 246,278,286,306,334,343,370,378,384,400,404,420,422,449,462,481,483,
%U 499,509,537,551,568,587,590,609,651,652,667,684,730,755,761,806,817,825,827,848,867,870,882,916,931,980,982,992
%N Numbers n such that N = (5n)^2 is a twin rank (cf. A002822: 6N +- 1 are twin primes).
%C Dinculescu notes that if N = m^2 > 1 is a twin rank (i.e., in A002822), then m is always a multiple of 5, and if N = m^3 > 1, then m is a multiple of 7, cf. A326234. He asks whether there are other pairs (a, b) different from (5, 2) and (7, 3) such that all twin ranks m^b > 1 are of the form m = a*n. (Of course (5, 2) and (7, 3) imply that (5, 2k), (7, 3k) and (35, 6k) is such a pair for any k.) This sequence lists the n for (a, b) = (5, 2), see A326232 for the numbers m.
%C See A326233, A326234 for m^3 and A326235, A326236 for m^6.
%H M. F. Hasler, <a href="/A326231/b326231.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 a(n) = A326232(n+1)/5.
%o (PARI) select( is(n)=!for(s=1,2,ispseudoprime(150*n^2+(-1)^s)||return), [1..10^3])
%Y Cf. A002822, A326232 ({1} U {5*a(n)}), A326233 (analog for m^3), A326234, A326235 (analog for m^6), A326230 (least twin rank n^k > 1 for given k).
%K nonn
%O 1,2
%A _M. F. Hasler_ and _Antonie Dinculescu_, Jun 14 2019
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