A340210 a(n) is the least k > 0 such that k*prime(n)+prime(n+1) and k*prime(n)+prime(n+2) are both prime.

1, 2, 6, 18, 6, 48, 12, 2, 36, 8, 6, 30, 66, 12, 22, 66, 18, 96, 18, 8, 30, 6, 24, 60, 114, 114, 138, 30, 66, 12, 18, 42, 54, 120, 14, 6, 48, 38, 22, 180, 78, 6, 30, 18, 14, 24, 6, 18, 12, 6, 36, 12, 2, 66, 4, 240, 18, 12, 60, 150, 78, 84, 90, 126, 42, 18, 36, 30, 12, 36, 24, 14, 24, 6, 6, 84, 48

Offset

1,2

Comments

a(n) is even for n > 1.

a(n) = 2 for n in A340225.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For n=3, prime(3)=5, prime(4)=7, prime(5)=11, and 6*5+7= 37 and 6*5+11=41 are prime, so a(3)=6.

Maple

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

Crossrefs

Cf. A340211, A340212, A340225.

Sequence in context: A183757 A356011 A181490 * A165325 A316765 A097635

Adjacent sequences: A340207 A340208 A340209 * A340211 A340212 A340213

Keyword

nonn

Author

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

Status

approved