A340777 a(n) is the first prime p such that p*2^n+q*3^n and p*3^n+q*2^n are both prime, where q is the prime following p.

2, 5, 5, 5, 67, 5, 7, 19, 107, 61, 67, 7, 5, 103, 263, 13, 83, 197, 17, 1097, 709, 103, 2731, 367, 271, 353, 1951, 43, 1109, 113, 457, 131, 67, 197, 1427, 199, 379, 7, 1901, 367, 3889, 8387, 97, 367, 2297, 613, 89, 6263, 2017, 127, 2647, 911, 8831, 45949, 4051, 2671, 2927, 883, 4423, 4027, 11

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..1337

Example

a(3) = 5 because 5*2^3+7*3^3 = 229 and 5*3^n+7*2^n = 191 are prime.

Maple

f:= proc(n) local p, q;
  q:= 2;
  do
    p:= q; q:= nextprime(q);
    until isprime(p*2^n+q*3^n) and isprime(p*3^n + q*2^n);
  p
end proc:
map(f, [$0..100]);

Mathematica

fpp[n_]:=Module[{p=2}, While[!PrimeQ[p 2^n+NextPrime[p]3^n]|| !PrimeQ[p 3^n+ NextPrime[ p]2^n], p=NextPrime[p]]; p]; Array[fpp, 70, 0] (* Harvey P. Dale, Jun 29 2021 *)

Prog

(PARI) a(n) = my(p=2, q=nextprime(p+1)); while(! (isprime(p*2^n+q*3^n) && isprime(p*3^n + q*2^n)), p=q; q=nextprime(p+1)); p; \\ Michel Marcus, Jan 21 2021

Crossrefs

Cf. A340694.

Sequence in context: A082086 A082084 A094236 * A205444 A270705 A073101

Adjacent sequences: A340774 A340775 A340776 * A340778 A340779 A340780

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 21 2021

Status

approved