A108580 Numbers whose sum of bits when written in binary > sum of decimal digits.

10, 11, 30, 31, 100, 101, 102, 103, 110, 111, 120, 121, 200, 201, 210, 211, 220, 221, 300, 301, 310, 311, 500, 501, 510, 511, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1010, 1011, 1012, 1013, 1014, 1015, 1020, 1021, 1022, 1023, 1100, 1101, 1102, 1103

Offset: 1

Author

John L. Drost, Jul 25 2005

Keywords

• nonn
• base

Comments

The sequence is infinite because 10^n, n = 1,2,3, .... are terms. - Marius A. Burtea, Sep 07 2019

Examples

			1103 is on the list since 1103 is 10001001111 (sum=6), 1+1+0+3=5.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..5000

Crossrefs

Subsequence of A325483.

Cf. A000120, A007953, A037308.

Programs

Magma

[n:n in [1..1200]| &+Intseq(n,2) gt &+Intseq(n,10)];  // Marius A. Burtea, Sep 07 2019

Mathematica

Select[Range[1103], Total@IntegerDigits[#, 2] > Total@IntegerDigits[#, 10] &] (* Amiram Eldar, Sep 07 2019 *)

PARI

isok(n) = hammingweight(n) > sumdigits(n); \\ Michel Marcus, Sep 07 2019

Python

def ok(n): return sum(map(int, str(n))) < bin(n).count('1')
print(list(filter(ok, range(1104)))) # Michael S. Branicky, Oct 11 2021

Extensions

a(36) added by Marius A. Burtea, Sep 07 2019