A178659 Numbers n such that n^2 +- (n-1)^2 are primes.

2, 3, 6, 10, 15, 30, 31, 36, 40, 51, 66, 70, 91, 100, 136, 175, 190, 205, 225, 231, 261, 285, 286, 316, 321, 331, 370, 376, 411, 441, 465, 496, 516, 520, 526, 535, 546, 565, 576, 586, 591, 681, 720, 730, 745, 750, 766, 855, 871, 906, 916, 951, 975, 1081, 1120

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 01 2010

Keywords

• nonn

Examples

			2 is in the sequence because 2^2 + 1^2 = 5 and 2^2 - 1^2 = 3 are both prime.
3 is in the sequence because 3^2 + 2^2 = 13 and 3^2 - 2^2 = 5 are both prime.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A068501.

Programs

Mathematica

lst={};Do[If[PrimeQ[n^2-(n-1)^2]&&PrimeQ[n^2+(n-1)^2],AppendTo[lst,n]],{n,7!}];lst
Select[Range[8!], PrimeQ[#^2 -(#-1)^2] && PrimeQ[#^2 +(#-1)^2] &] (* G. C. Greubel, Jan 28 2019 *)

PARI

A178659()={my(maxx=1000);n=2;ptr=0;
while(n<=maxx,q1=n^2-(n-1)^2;q2=n^2+(n-1)^2;
if(isprime(q1)&&isprime(q2),ptr++;write("b178659.txt",ptr,"  ",n));n++); } \\ Bill McEachen, Jun 13 2014

Formula

a(n) = 1 + A068501(n). - Zak Seidov, Feb 10 2015