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, 8388608, 16777216

Offset

1,2

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..69

Formula

Union of A162363 and the powers of 2.

Mathematica

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<n, k++ ]; s== n]]; Select[Range[3000], IsKeith2[ # ]&]

Crossrefs

Cf. A007629 (base 10), this sequence (base 2), A187713 (base 5), A188195-A188200 (bases 3-4 and 6-9), A162363.

Sequence in context: A126294 A339973 A224912 * A244750 A140974 A349763

Adjacent sequences: A162721 A162722 A162723 * A162725 A162726 A162727

Keyword

base,nonn

Author

T. D. Noe, Jul 11 2009

Extensions

a(40)-a(41) from Amiram Eldar, Jan 20 2026

Status

approved