A153085 - OEIS

%I #14 Sep 08 2022 08:45:39

%S 1,4,5,7,10,11,13,15,16,18,19,20,22,25,28,29,30,31,32,34,35,37,39,40,

%T 41,43,45,46,49,50,51,52,53,54,55,58,60,61,62,64,65,67,70,71,73,74,75,

%U 76,79,80,81,82,84,85,88,89,90,91,93,94,95,97,100,102,103,105,106

%N Numbers k such that 4*k + 5 is not prime.

%C Let p=2n+1 be an odd number, then A140869(n,n) = (p^2-5)/4 = A028387(n-1).

%C One less than the associated entry in A045751: a(n) = A045751(n+1)-1. - _R. J. Mathar_, Jan 05 2011

%H Vincenzo Librandi, <a href="/A153085/b153085.txt">Table of n, a(n) for n = 1..1000</a>

%e Triangle begins:

%e 1;

%e *, 5;

%e 4, *, 11;

%e *, 10, *, 19;

%e 7, *, 18, *, 29;

%e *, 15, *, 28, *, 41;

%e where * mark the entries in A140869 which are non-integer if floor(.) is not applied there.

%t Select[Range[200], !PrimeQ[4 # + 5] &] (* _Vincenzo Librandi_, Oct 15 2012 *)

%o (Magma) [n: n in [1..120] | not IsPrime(4*n + 5)]; // _Vincenzo Librandi_, Oct 15 2012

%Y Cf. A028387, A045751, A111215, A140869.

%K nonn

%O 1,2

%A _Vincenzo Librandi_, Dec 18 2008