A154734 Define k(0) = 2 and k(m) = m^2-k(m-1) for m >= 1. This is a list of those terms k(m) for which k(m)+1 and k(m)-1 are both in A008578 (primes including 1).

2, 4, 12, 138, 822, 2082, 3918, 21738, 39342, 62130, 70878, 106032, 117372, 129288, 135462, 182712, 512580, 524802, 575130, 682698, 769422, 799482, 893118, 1008912, 1026030, 1043292, 1828830, 2368578, 2447580, 3247428, 3278082, 3465030, 4022868, 4056978

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 14 2009

Keywords

• nonn

Crossrefs

Cf. A008578, A154736.

Programs

Maple

a := proc(n) local k; k := n*(n - 1)/2 - 2*(-1)^n:
if k = 2 or isprime(k - 1) and isprime(k + 1) then k else NULL fi end:
seq(a(n), n = 1..1000);  # Peter Luschny, Jul 14 2022

Mathematica

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

PARI

a154734(upto,k0=2) = {my(k=k0); print1(k,", "); for(n=1, oo, my(kk=n^2-k);if(isprime(k-1) && isprime(k+1), print1(k,", ")); k=kk; if(k>upto, break))};
a154734(5000000) \\ Hugo Pfoertner, Jul 14 2022

Formula

k(n) = n*(n+1)/2+2*(-1)^n. - Peter Luschny, Jul 14 2022

Extensions

Better name from Pontus von Brömssen, Jul 14 2022