A153115 Positive integers with the same number of 1s in base 10 and base 2.

1, 16, 128, 512, 1024, 1152, 2112, 4112, 8192, 16384, 16416, 16512, 131073, 131074, 131076, 131080, 131081, 131088, 131105, 131106, 131108, 131110, 131111, 131113, 131114, 131116, 131120, 131121, 131137, 131138, 131140, 131141, 131144, 131152

Offset

1,2

Comments

Some have exactly one 1. These are exclusively of the form 2^n, but not universally. 512 = 1000000000b, 1 one. 2048 = 100000000000b but 2048 lacks a 1 digit. The smallest integer with 6 ones in both decimal and binary bases is 11011112 = 101010000000010000101000b.

If n is in the sequence and n == 0, 5, 9, 10, 13 or 17 (mod 20) or 11 (mod 40), then n+1 is in the sequence. - Robert Israel, Jun 17 2020

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 250 terms from Robert Israel)

Example

a(6)=1152 because 1152 base 2 = 10010000000 and both terms have the same number of ones.

Maple

filter:= proc(n) numboccur(1, convert(n, base, 2))=numboccur(1, convert(n, base, 10)) end proc:
select(filter, [$1..2*10^5]); # Robert Israel, Jun 16 2020

Crossrefs

Cf. A000120.

Sequence in context: A291460 A004017 A167471 * A138331 A290031 A008535

Adjacent sequences: A153112 A153113 A153114 * A153116 A153117 A153118

Keyword

base,nonn,look

Author

Gil Broussard, Dec 18 2008

Status

approved