A212283 First a(n) > 1 whose sum of digits is the same in base 2 as in base n.

2, 6, 4, 6, 12, 21, 8, 10, 20, 12, 14, 172, 30, 46, 16, 18, 36, 20, 22, 126, 46, 24, 26, 126, 28, 30, 58, 60, 120, 126, 32, 34, 68, 36, 38, 185, 78, 40, 42, 126, 44, 46, 90, 92, 138, 48, 50, 246, 52, 54, 106, 108, 56, 58, 114, 60, 62, 120, 182, 126, 188, 378

Offset

2,1

Comments

Theoretically, there might exist an n for which there is no solution, in which case a(n) would be set to 0 by convention; however, no such case was found so far. Problem: does it exist?

Links

Stanislav Sykora, Table of n, a(n) for n = 2..10000

Example

Example: a(13) = 172 because 172 is the first number >1 such that its expansions in base 2 (10101100) and in base 13 (103) have the same sum of digits, namely 4.

Mathematica

sdn[n_]:=Module[{a=2}, While[Total[IntegerDigits[a, 2]]!=Total[ IntegerDigits[ a, n]], a++]; a]; Array[sdn, 70, 2] (* Harvey P. Dale, May 29 2013 *)

Crossrefs

Cf. A037301, A212222.

Sequence in context: A059773 A127399 A240751 * A247566 A151689 A216833

Adjacent sequences: A212280 A212281 A212282 * A212284 A212285 A212286

Keyword

nonn,base

Author

Stanislav Sykora, May 08 2012

Status

approved