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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A068501.

Sequence in context: A280421 A369425 A018141 * A268064 A077011 A246868

Adjacent sequences: A178656 A178657 A178658 * A178660 A178661 A178662

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 01 2010

Status

approved