A154736 - OEIS

%I #27 Jul 18 2022 19:29:07

%S 3,4,16,40,64,88,208,280,352,376,460,484,508,520,604,1012,1024,1072,

%T 1168,1240,1264,1336,1420,1432,1444,1912,2176,2212,2548,2560,2632,

%U 2836,2848,2872,2944,2956,3184,3220,3508,3616,3640,3772,3868,3892,3928,3940,3952

%N 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.

%H Michael De Vlieger, <a href="/A154736/b154736.txt">Table of n, a(n) for n = 1..10000</a>

%F A154734(n+1) = k(a(n)) where k(m) = m*(m+1)/2+2*(-1)^m. - _R. J. Mathar_, Jul 16 2022

%e The initial values of k(m) are:

%e k(0) = 2

%e k(1) = 1-2 = -1

%e k(2) = 4+1 = 5

%e k(3) = 9-5 = 4 and both 3 and 5 are primes, so 3 is the first term in the sequence

%e k(4) = 16-4 = 12, and 11 & 13 are primes, so a(2) = 4

%e   and so on - _N. J. A. Sloane_, Jul 14 2022

%t k=2;lst={};Do[k=n^2-k;If[PrimeQ[k-1]&&PrimeQ[k+1],AppendTo[lst,n]],{n,8!}];lst

%t (* Second program: *)

%t 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 *)

%o (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)};

%o a154736(5000) \\ _Hugo Pfoertner_, Jul 14 2022

%Y Cf. A154734.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 14 2009

%E Better name from _Pontus von Brömssen_, Jul 14 2022