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

1,1

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A154734.

Sequence in context: A328773 A330693 A329541 * A188114 A188116 A300316

Adjacent sequences: A154733 A154734 A154735 * A154737 A154738 A154739

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 14 2009

Extensions

Better name from Pontus von Brömssen, Jul 14 2022

Status

approved