A276495 Odd numbers not of the form p + 2^m with p prime and m >= 0 for which the smallest k in A067760 such that n + 2^k is prime increases.

1, 127, 251, 1657, 1777, 1973, 3181, 21893, 31951, 50839, 67607, 138977

Offset: 1

Author

Arkadiusz Wesolowski, Sep 05 2016

Keywords

• nonn
• hard
• more

Comments

There exist de Polignac numbers n such that for all k >= 1 the numbers n + 2^k are composite. It is conjectured that 30666137 is the smallest such number.

a(13) >= 453143.

Crossrefs

Cf. A006285, A067760, A263644.

A276496 gives the record values.

Programs

Magma

lst:=[]; c:=0; for n in [1..31951 by 2] do m:=-1; repeat m+:=1; a:=n-2^m; until a lt 1 or IsPrime(a); if a lt 1 then k:=0; repeat k+:=1; b:=n+2^k; until IsPrime(b); if k gt c then Append(~lst, n); c:=k; end if; end if; end for; lst;