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
Keywords
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
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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