A154736 Define k(0) = 2 and k(m) = m^2-k(m-1) for m >= 1. This is a list of those m for which k(m)+1 and k(m)-1 are both prime.

3, 4, 16, 40, 64, 88, 208, 280, 352, 376, 460, 484, 508, 520, 604, 1012, 1024, 1072, 1168, 1240, 1264, 1336, 1420, 1432, 1444, 1912, 2176, 2212, 2548, 2560, 2632, 2836, 2848, 2872, 2944, 2956, 3184, 3220, 3508, 3616, 3640, 3772, 3868, 3892, 3928, 3940, 3952

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 14 2009

Keywords

• nonn

Examples

			The initial values of k(m) are:
k(0) = 2
k(1) = 1-2 = -1
k(2) = 4+1 = 5
k(3) = 9-5 = 4 and both 3 and 5 are primes, so 3 is the first term in the sequence
k(4) = 16-4 = 12, and 11 & 13 are primes, so a(2) = 4
  and so on - _N. J. A. Sloane_, Jul 14 2022
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A154734.

Programs

Mathematica

k=2;lst={};Do[k=n^2-k;If[PrimeQ[k-1]&&PrimeQ[k+1],AppendTo[lst,n]],{n,8!}];lst
(* Second program: *)
k = 2; Reap[Do[Set[k, m^2 - k]; If[AllTrue[k + {-1, 1}, PrimeQ], Sow[m]], {m, 4000}]][[-1, -1]] (* Michael De Vlieger, Jul 14 2022 *)

PARI

a154736(upto,k0=2) = {my(k=k0); for(n=1, upto, my(kk=n^2-k); if(isprime(kk-1) && isprime(kk+1), print1(n,", ")); k=kk)};
a154736(5000) \\ Hugo Pfoertner, Jul 14 2022

Formula

A154734(n+1) = k(a(n)) where k(m) = m*(m+1)/2+2*(-1)^m. - R. J. Mathar, Jul 16 2022

Extensions

Better name from Pontus von Brömssen, Jul 14 2022