A265426 Primes p such that p - 1 is a binary Keith number (A162724).

2, 3, 5, 17, 257, 1367, 65537, 2960687

Offset: 1

Author

Jaroslav Krizek, Dec 08 2015

Keywords

• nonn
• more

Comments

See A162724 (binary Keith numbers) and A007629 (Keith numbers) for definitions.

Primes of the form A162724(n)+1.

Fermat primes (A019434) are terms.

The next term, if it exists, must be greater than 17*10^9.

Union of primes p of the form A162363(n)+1 and A000079(m)+1 for a some n or m.

Crossrefs

Cf. A000079, A007629, A019434, A162363, A162724.

Programs

Mathematica

fQ[n_] := Module[{b = IntegerDigits[n, 2], s}, s = Total@ b; If[s <= 1, True, k = 1; While[s = 2 s - b[[k]]; s < n, k++]; s == n]]; Select[Prime@ Range[10^6], fQ[# - 1] &] (* Michael De Vlieger, Dec 09 2015, after T. D. Noe at A162724 *)