A162363 -id:A162363 - cp's OEIS frontend

A162724 Binary Keith numbers.

1, 2, 3, 4, 8, 16, 32, 64, 128, 143, 256, 285, 512, 569, 683, 1024, 1138, 1366, 2048, 2276, 4096, 8192, 16384, 32768, 65536, 131072, 154203, 262144, 308405, 524288, 616810, 678491, 1048576, 1356981, 1480343, 2097152, 2713962, 2960686, 4194304

Offset: 1

T. D. Noe, Jul 11 2009

See A162363. It is easy to see that every power of 2 is a binary Keith number.

IsKeith2[n_Integer] := Module[{b,s}, b=IntegerDigits[n,2]; s=Total[b]; If[s<=1, True, k=1; While[s=2*s-b[[k]]; s

Union of A162363 and the powers of 2.

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

Original entry on oeis.org

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

Offset: 1

Jaroslav Krizek, Dec 08 2015

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.

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

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 *)

cp's OEIS Frontend

A162724 Binary Keith numbers.

Views

Author

Keywords

Comments

Programs

Mathematica

Formula