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Numbers k such that either k*(k+1)/4 + 1 or k*(k+1)/4 - 1 or both are primes.
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%I #13 Jul 18 2021 06:49:36

%S 3,7,8,15,16,23,24,32,39,40,47,48,55,56,63,64,71,79,80,87,95,103,104,

%T 111,112,119,120,128,135,136,143,151,152,159,167,175,176,183,199,208,

%U 216,223,224,231,232,239,240,247,248,255,256,263,264,271,279,287,288

%N Numbers k such that either k*(k+1)/4 + 1 or k*(k+1)/4 - 1 or both are primes.

%C The primes are (sum of numbers from 1 to k)/2 + or - 1.

%H Amiram Eldar, <a href="/A105173/b105173.txt">Table of n, a(n) for n = 1..10000</a>

%e 3*4/4 = 3, 3-1 = 2 is prime so a(1) = 3.

%e 7*8/4 = 14, 14-1 = 13 is prime so a(2) = 7.

%e 8*9/4 = 18, 18-1 = 17 is prime, 18+1 = 19 is prime, so a(3) = 8.

%t Select[Range[300], Or @@ PrimeQ[#*(#+1)/4 + {-1, 1}] &] (* _Amiram Eldar_, Jul 18 2021 *)

%Y Subsequence of A014601.

%K nonn

%O 1,1

%A _Pierre CAMI_, Apr 11 2005

%E More terms from _Amiram Eldar_, Jul 18 2021