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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(PARI) isok(n) = hammingweight(n) > sumdigits(n); \\ Michel Marcus, Sep 07 2019
(Magma) [n:n in [1..1200]| &+Intseq(n, 2) gt &+Intseq(n, 10)];  // Marius A. Burtea, 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

Crossrefs

Subsequence of A325483.

Cf. A000120, A007953, A037308.

Sequence in context: A086458 A179856 A098795 * A356279 A041208 A041485

Adjacent sequences: A108577 A108578 A108579 * A108581 A108582 A108583

Keyword

nonn,base

Author

John L. Drost, Jul 25 2005

Extensions

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

Status

approved