A195465 The first a(n) n-gap primes are lessers of twin primes, a(n) maximal.

0, 5, 5, 17, 5, 6, 14, 6, 24, 75, 2, 4, 27, 11, 48, 50, 46, 9, 21, 7, 16, 137, 4, 55, 85, 14, 111, 24, 102, 291, 67, 89, 155, 180, 137, 330, 127, 413, 250, 241, 332, 619, 139, 234, 453, 929, 94, 160, 169, 22, 131, 434

Offset

1,2

Comments

For definition of n-gap primes, see comment to A195270.

Conjecture: a(n)>0 for n>1. This conjecture is equivalent to the conjecture that all terms of A195325 are lessers of twin primes.

Links

Table of n, a(n) for n=1..52.

Maple

a:= proc(n) local i, p, q;
      p, q:= 2, 3;
      for i from 0 do
        while nextprime(n*p) < (n*q) do
          p, q:= q, nextprime(q)
        od;
        if not isprime(p+2) then return i fi;
        p, q:= q, nextprime(q)
      od
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Sep 20 2011

Mathematica

a[n_] := a[n] = Module[{i, p = 2, q = 3}, For[i = 0, True, i++, While[NextPrime[n p] < n q, p = q; q = NextPrime[q]]; If[!PrimeQ[p+2], Return[i]]; p = q; q = NextPrime[q]]];
Array[a, 20] (* Jean-François Alcover, Nov 21 2020, after Alois P. Heinz *)

Crossrefs

Cf. A195325, A080192, A195270, A195271, A164368, A194658, A164294.

Sequence in context: A356049 A154232 A194615 * A173464 A072272 A273502

Adjacent sequences: A195462 A195463 A195464 * A195466 A195467 A195468

Keyword

nonn

Author

Vladimir Shevelev, Sep 19 2011

Status

approved