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

1,1

Links

Table of n, a(n) for n=1..34.

Formula

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

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

Prog

(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

Crossrefs

Cf. A008578, A154736.

Sequence in context: A154882 A062000 A053040 * A291827 A287059 A059085

Adjacent sequences: A154731 A154732 A154733 * A154735 A154736 A154737

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 14 2009

Extensions

Better name from Pontus von Brömssen, Jul 14 2022

Status

approved