|
%I #16 Jul 17 2021 11:24:26
%S 1,1820,2590,4795,5565,8330,8470,10640,10710,15960,16730,19145,24535,
%T 26460,34580,37065,41510,42630,43505,48230,59675,69160,84910,90860,
%U 99540,103320,112560,114205,117600,127120,129220,131670,143290,152740,161105,164115,170030,175105,181195,185045
%N Numbers k such that N = k^6 is a twin rank (cf. A002822: 6N +- 1 are twin primes).
%C Dinculescu notes that when N = m^2 (resp. m^3) > 1 is a twin rank (i.e., in A002822), then m is a multiple of 5 (resp. of 7), cf. A326232 and A326234. Thus, when N = m^6, then m is a multiple of 35. See A326235 for a(n)/35, n > 1.
%C See A326232 and A326231 for m^2, A326234 and A326233 for m^3.
%H M. F. Hasler, <a href="/A326236/b326236.txt">Table of n, a(n) for n = 1..10001</a> (3667 terms from A. Dinculescu).
%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) = 35*A326235(n-1), n >= 2.
%o (PARI) select( is(n)=!for(s=1,2,ispseudoprime(6*n^6+(-1)^s)||return), [1..10^5])
%Y Cf. A002822, A326235 (a(n)/35, n>1), A326231, A326232 (analog for n^2), A326233, A326234 (analog for n^3), A326230 (least twin rank n^k for given k).
%K nonn
%O 1,2
%A _M. F. Hasler_ and _Antonie Dinculescu_, Jun 14 2019
|
