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

1,3

Comments

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

Links

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

Formula

From Reinhard Zumkeller, Aug 06 2010: (Start)

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

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

Example

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

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 *)

Prog

(PARI) is(n)=hammingweight(n)==sumdigits(n); \\ Charles R Greathouse IV, Sep 25 2012
(Sage) [n for n in (0..10000) if sum(n.digits(base=2)) == sum(n.digits(base=10))] # Freddy Barrera, Oct 12 2018
(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

Crossrefs

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

Sequence in context: A041826 A041824 A309829 * A041828 A041830 A041832

Adjacent sequences: A037305 A037306 A037307 * A037309 A037310 A037311

Keyword

nonn,base

Author

Clark Kimberling

Extensions

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

Status

approved