A340212 a(n) is the least k > 0 such that k*prime(n)+prime(n-1) and k*prime(n)+prime(n+1) are both prime.

2, 6, 6, 2, 2, 6, 6, 24, 12, 24, 20, 12, 12, 28, 12, 24, 66, 20, 24, 6, 6, 6, 14, 36, 2, 14, 20, 8, 18, 12, 54, 6, 38, 102, 10, 120, 42, 28, 42, 38, 8, 20, 2, 18, 10, 12, 2, 6, 6, 114, 32, 36, 4, 24, 12, 120, 36, 14, 32, 18, 8, 74, 20, 54, 30, 90, 36, 6, 6, 54, 30, 40, 6, 6, 24, 26, 32, 8, 12, 12

Offset

3,1

Comments

All terms are even.

a(n) = 2 if and only if prime(n) is in A125146.

Links

Robert Israel, Table of n, a(n) for n = 3..10000

Example

For n=3, prime(2)=3, prime(3)=5, prime(4)=7, and 2*5+3=13 and 2*5+7=17 are prime, so a(3)=2.

Maple

f:= proc(n) local p, q, r, k;
  p:= ithprime(n);
  q:= ithprime(n-1);
  r:= ithprime(n+1);
  for k from 2 by 2 do
    if isprime(k*p+q) and isprime(k*p+r) then return k fi
  od
end proc:
map(f, [$3..100]);

Prog

(PARI) a(n) =  my(p=prime(n), k=1); while (! (isprime(k*p+precprime(p-1)) && isprime(k*p+nextprime(p+1))), k++); k; \\ Michel Marcus, Jan 01 2021

Crossrefs

Cf. A125146, A340210, A340214.

Sequence in context: A242001 A175994 A372985 * A283613 A141327 A248011

Adjacent sequences: A340209 A340210 A340211 * A340213 A340214 A340215

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 31 2020

Status

approved