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A056906 Numbers k such that 36*k^2 + 5 is prime. 6

%I #24 Sep 08 2022 08:45:01

%S 0,1,2,6,8,12,13,16,19,21,27,28,33,34,41,43,49,56,57,62,69,72,76,77,

%T 82,84,86,89,92,96,98,99,104,111,119,121,126,128,131,132,133,134,139,

%U 142,146,148,153,159,166,168,169,173,174

%N Numbers k such that 36*k^2 + 5 is prime.

%C Except for a(1), a(n) is never a multiple of 5.

%H Vincenzo Librandi, <a href="/A056906/b056906.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = sqrt(A056905(n)-5)/6.

%e a(3)=2 since 36*2^2 + 5 = 149, which is prime.

%t Select[Range[0,200],PrimeQ[36#^2+5]&] (* _Harvey P. Dale_, Jul 25 2011 *)

%o (Magma) [n: n in [0..200]| IsPrime(36*n^2+5)]; // _Vincenzo Librandi_, Jul 14 2012

%o (PARI) is(n)=isprime(36*n^2+5) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y This sequence and formula generate all primes of the form k^2+5, i.e., A056905.

%Y Except for the first term, this sequence is a subsequence of A047201.

%Y Cf. A056900, A056902.

%K nonn,easy

%O 1,3

%A _Henry Bottomley_, Jul 07 2000

%E Offset corrected by _Arkadiusz Wesolowski_, Aug 09 2011

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)