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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.

%I A154736 #27 Jul 18 2022 19:29:07
%S A154736 3,4,16,40,64,88,208,280,352,376,460,484,508,520,604,1012,1024,1072,
%T A154736 1168,1240,1264,1336,1420,1432,1444,1912,2176,2212,2548,2560,2632,
%U A154736 2836,2848,2872,2944,2956,3184,3220,3508,3616,3640,3772,3868,3892,3928,3940,3952
%N 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.
%H A154736 Michael De Vlieger, <a href="/A154736/b154736.txt">Table of n, a(n) for n = 1..10000</a>
%F A154736 A154734(n+1) = k(a(n)) where k(m) = m*(m+1)/2+2*(-1)^m. - _R. J. Mathar_, Jul 16 2022
%e A154736 The initial values of k(m) are:
%e A154736 k(0) = 2
%e A154736 k(1) = 1-2 = -1
%e A154736 k(2) = 4+1 = 5
%e A154736 k(3) = 9-5 = 4 and both 3 and 5 are primes, so 3 is the first term in the sequence
%e A154736 k(4) = 16-4 = 12, and 11 & 13 are primes, so a(2) = 4
%e A154736   and so on - _N. J. A. Sloane_, Jul 14 2022
%t A154736 k=2;lst={};Do[k=n^2-k;If[PrimeQ[k-1]&&PrimeQ[k+1],AppendTo[lst,n]],{n,8!}];lst
%t A154736 (* Second program: *)
%t A154736 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 A154736 (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 a154736(5000) \\ _Hugo Pfoertner_, Jul 14 2022
%Y A154736 Cf. A154734.
%K A154736 nonn
%O A154736 1,1
%A A154736 _Vladimir Joseph Stephan Orlovsky_, Jan 14 2009
%E A154736 Better name from _Pontus von Brömssen_, Jul 14 2022