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%I #12 Jun 22 2019 21:27:42
%S 1,28,42,168,203,287,308,518,1043,1057,1512,1603,1638,1680,1757,1988,
%T 2905,3367,3927,4018,4928,5033,5145,5257,5292,5432,5733,6762,7182,
%U 7210,7798,8715,10213,10318,10668,10745,11088,12243,13552,14245,14588,14707,15155,15323,15687,15722,15757
%N Numbers n such that N = n^3 is a twin rank (A002822: 6N +- 1 are twin primes).
%C Dinculescu notes that when n^2 or n^3 is a twin rank > 1 (i.e., in A002822), then n is a multiple of 5, resp. 7. It is unknown whether there exist other pairs (a, b) different from (5, 2) and (7, 3) such that n^b => a | n. (Of course (5, 2k) and (7, 3k) and (35, 6k) is a solution for any k.) See A326233 for the terms > 1 divided by 7.
%C See A326232 and A326231 for the case n^2, A326236 and A326235 for n^6.
%H A. Dinculescu, <a href="/A326234/b326234.txt">Table of n, a(n) for n = 1..14709</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) = 7*A326233(n-1), n >= 2.
%o (PARI) select( is(n)=!for(s=1,2,ispseudoprime(6*n^3+(-1)^s)||return), [1..10^5])
%Y Cf. A002822, A326233 (a(n)/7, n>1), A326231, A326232 (analog for n^2), A326235, A326236 (analog for n^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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