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

Author

Stanislav Sykora, May 08 2012

Keywords

• nonn
• base

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?

Examples

			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.
		

Links

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

Crossrefs

Cf. A037301, A212222.

Programs

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 *)