A078699 Primes p such that p^2-1 is a triangular number.

2, 11, 23, 373, 12671, 901273, 19472752251611, 53072032161200090602953513048447623, 5027153581127740201460650182713355379768873, 11604855412241025458500993236724193227031777965785837784548351709747881343573

Offset: 1

Author

Jason Earls, Dec 18 2002

Keywords

• nonn

Comments

Equivalently, primes in A006452.

The sequence of corresponding triangular numbers begins 3, 120, 528, 139128, 160554240, 812293020528, 379188080252621270252095320, ... [Shreevatsa R, Jul 12 2013]

Links

• Joerg Arndt, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A000217, A006452.

Programs

Mathematica

a[n_] := a[n]=If[n<4, {1, 2, 4, 11}[[n+1]], 6a[n-2]-a[n-4]]; Select[a/@Range[200], ProvablePrimeQ] (* First do <
				

PARI

default(primelimit,10^7) istri(n) = t=floor(sqrt(2*n)); if(2*n==t*(t+1),1,0) forprime(p=2,5*10^6,if(istri(p^2-1),print1(p" ")))

PARI

istriang(n)=issquare(8*n+1);
forprime(p=2,10^10,if(istriang(p^2-1),print1(p,", ")));
\\ Joerg Arndt, Jul 15 2013

PARI

/* much more efficient: */
N=1166; f=( 1+x-4*x^2-2*x^3 ) / ( (x^2+2*x-1)*(x^2-2*x-1) )+O(x^N);
for(n=0,N-1,my(c=polcoeff(f,n)); if(isprime(c), print1(c,", ")));
\\ Joerg Arndt, Jul 15 2013

Extensions

Edited by Dean Hickerson, Dec 19 2002