A340226 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, 4, 4, 6, 6, 4, 42, 18, 6, 6, 10, 10, 6, 2, 120, 18, 12, 6, 6, 30, 6, 24, 70, 6, 18, 60, 6, 66, 52, 30, 6, 42, 18, 366, 2, 6, 6, 2, 18, 18, 12, 40, 30, 6, 2, 78, 66, 36, 66, 6, 42, 54, 2, 2, 36, 90, 60, 36, 18, 48, 6, 6, 46, 42, 90, 24, 4, 6, 126, 6, 60, 2, 150, 156, 30, 144, 30, 48, 30, 100, 4

Offset

3,1

Comments

All terms are even.

Links

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

Example

For n = 4, 5, 7 and 11 are the third to fifth primes, 4*7-5 = 23 and 4*7-11 = 17 are prime, so a(4)=4.

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]);

Mathematica

lkp[p_]:=Module[{a=NextPrime[p, -1], b=NextPrime[p], k=2}, While[Total[Boole[ PrimeQ[ k p-{a, b}]]]!=2, k=k+2]; k]; lkp/@Prime[Range[3, 90]] (* Harvey P. Dale, Feb 23 2023 *)

Crossrefs

Cf. A340212.

Sequence in context: A266076 A074325 A058249 * A348769 A058043 A251546

Adjacent sequences: A340223 A340224 A340225 * A340227 A340228 A340229

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 01 2021

Status

approved