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A158036 Integer solutions f for f = (4^n - 2^n + 8n^2 - 2) / (2n * (2n + 1)) with n an integer.

%I A158036 #10 Jun 24 2024 22:27:23
%S A158036 3,8287,32547981403,3374074914839397834392750148706282243018046503,
%T A158036 107547872626305931371847778721098686654377801057464206176785452350259573207,
%U A158036 4568366860875634575966528292411682488942909674818941246717098803707597353756388768388059303363024343431
%N A158036 Integer solutions f for f = (4^n - 2^n + 8n^2 - 2) / (2n * (2n + 1)) with n an integer.
%C A158036 8287 = 129 * 64 + 31 = 257 * 32 + 63 is prime. A158034 (values of n) is often prime. A158035 (2n + 1) appears to be always prime.
%C A158036 See A235540 for nonprimes in A158034. - _Reinhard Zumkeller_, Nov 17 2014
%H A158036 Reinhard Zumkeller, <a href="/A158036/b158036.txt">Table of n, a(n) for n = 1..32</a>
%o A158036 (Haskell)
%o A158036 a158036 = (\x -> (4^x - 2^x + 8*x^2 - 2) `div` (2*x*(2*x + 1))) . a158034
%o A158036 -- _Reinhard Zumkeller_, Nov 17 2014
%Y A158036 Cf. A158034, A158035 (n, 2n + 1)
%Y A158036 Cf. A002515 (Lucasian primes)
%Y A158036 Cf. A145918 (exponential Sophie Germain primes)
%Y A158036 Cf. A235540.
%K A158036 nonn
%O A158036 1,1
%A A158036 _Reikku Kulon_, Mar 11 2009