A307775 Smallest k > 1 such that A014574(n)*k is in A014574.

3, 2, 5, 4, 2, 10, 3, 6, 10, 4, 6, 4, 9, 6, 15, 21, 13, 3, 15, 6, 6, 8, 6, 5, 4, 11, 5, 26, 6, 2, 2, 6, 6, 11, 4, 5, 4, 6, 14, 6, 20, 9, 46, 5, 9, 4, 14, 11, 9, 20, 21, 6, 6, 4, 6, 14, 4, 9, 9, 3, 21, 5, 35, 15, 14, 2, 5, 30, 36, 4, 5, 14, 2, 29, 21, 10, 39, 8, 4, 5, 9, 3

Offset: 1

Author

Dmitry Kamenetsky, Apr 28 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A014574.

Programs

Maple

P:= select(isprime, {seq(i,i=3..10^7,2)}):
A14574:= sort(convert(map(`+`,P,1) intersect map(`+`,P,-1),list)):
f:= proc(n) local k,v,kv;
  v:= A14574[n]:
  for k from 2 do
    kv:= k*v;
    if kv > 10^7 then if isprime(kv-1) and isprime(kv+1) then return k fi
    elif member(kv,A14574) then return k
    fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 17 2020

Mathematica

twinMidQ[n_] := AllTrue[{-1, 1} + n, PrimeQ]; f[n_] := Module[{k = 2}, While[! twinMidQ[k*n], k++]; k]; f /@ Select[Range[10^3], twinMidQ] (* Amiram Eldar, Jul 05 2019 *)

PARI

isok2(n) = isprime(n-1) && isprime(n+1);
k(n) = my(k=2); while (! isok2(n*k), k++); k;
lista(nn) = for (n=1, nn, if (isok2(n), print1(k(n), ", "))); \\ Michel Marcus, Apr 28 2019