A253108 - OEIS

%I #29 Aug 04 2022 18:29:34

%S 2,4,6,9,14,17,20,21,25,32,34,35,40,45,49,51,52,56,60,62,65,76,80,82,

%T 86,87,89,94,95,96,100,104,105,107,112,114,115,116,117,124,126,135,

%U 137,140,145,147,151,164,167,172,174,179,180,181,182,199,200,202,205,206,207

%N Numbers n such that (sum of n^2 through (n+2)^2) + (n+1)^2 is prime.

%C Sequence is related to the Legendre conjecture.

%C No terms == 3 mod 5 or == 1 mod 7 or 0 mod 11. - _Robert Israel_, Jun 24 2015

%H Robert Israel, <a href="/A253108/b253108.txt">Table of n, a(n) for n = 1..10000</a>

%e For n=2, n+1=3, n+2=4: we have

%e Sum(n^2,(n+1)^2)=Sum(2^2,3^2)=Sum(4,9)=Sum(4+5+6+7+8+9)=39,

%e Sum((n+1)^2,(n+2)^2)=Sum(3^2,4^2)=Sum(9,16)=Sum(9+10+11+12+13+14+15+16)=100,

%e 39+100=139,

%e 139 is prime; hence 2 is a term.

%p select(n -> isprime(4*n^3+14*n^2+20*n+11), [$1..1000]); # _Robert Israel_, Dec 28 2014

%t Select[Range[250],PrimeQ[Total[Range[#^2,(#+2)^2]]+(#+1)^2]&] (* _Harvey P. Dale_, Aug 04 2022 *)

%o (PARI)for (n=1,1000,if(isprime(4*n^3+14*n^2+20*n+11),print1(n",")))

%K nonn

%O 1,1

%A _César Aguilera_, Dec 26 2014

%E a(47) corrected by _Robert Israel_, Jun 24 2015