A037308 Numbers whose base-2 and base-10 expansions have the same digit sum.

0, 1, 20, 21, 122, 123, 202, 203, 222, 223, 230, 231, 302, 303, 410, 411, 502, 503, 1130, 1131, 1150, 1151, 1202, 1203, 1212, 1213, 1230, 1231, 1300, 1301, 1402, 1403, 1502, 1503, 1510, 1511, 2006, 2007, 2032, 2033, 2102, 2103, 2200, 2201, 3006, 3007, 3012

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

n is in the sequence iff n+(-1)^n is in the sequence. [Robert Israel, Mar 25 2013]

Examples

			122 is a member, since digital-sum_2(122) = 5 = digital-sum_10(122).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000120, A007953, A054899, A131451, A133620, A133900, A134599, A135110, A180018.

Programs

Maple

N:= 10000; # to get all elements up to N
select(x -> (convert(convert(x,base,10),`+`)-convert(convert(x,base,2),`+`)=0), [$0..N]); # Robert Israel, Mar 25 2013

Mathematica

Select[Range[0, 5000], Total[IntegerDigits[#, 2]] == Total[IntegerDigits[#, 10]] &] (* Jean-François Alcover, Mar 07 2016 *)

PARI

is(n)=hammingweight(n)==sumdigits(n); \\ Charles R Greathouse IV, Sep 25 2012

Python

def ok(n): return sum(map(int, str(n))) == sum(map(int, bin(n)[2:]))
print(list(filter(ok, range(3013)))) # Michael S. Branicky, Jun 20 2021

Sage

[n for n in (0..10000) if sum(n.digits(base=2)) == sum(n.digits(base=10))] # Freddy Barrera, Oct 12 2018

Formula

From Reinhard Zumkeller, Aug 06 2010: (Start)

A007953(a(n)) = A000120(a(n));

A180018(a(n)) = 0. (End)

Extensions

Edited by N. J. A. Sloane Nov 29 2008 at the suggestion of Zak Seidov