A153114 Integers with the same number of zeros in base 10 and base 2.

0, 1, 3, 7, 15, 30, 31, 63, 127, 255, 503, 507, 509, 510, 511, 1003, 1005, 1006, 1015, 1019, 1020, 1021, 1022, 2007, 2015, 2030, 2031, 2039, 2043, 2045, 2046, 3007, 3070, 3071, 4030, 4031, 4063, 4079, 4087, 4090, 4091, 4093, 4094, 8063, 8190, 8191, 16383

Offset

1,3

Comments

Some have no zeros at all. These are exclusively of the form 2^n-1, but not universally. 511=111111111b, no zeros. 1023=1111111111b but zero counts are inequal. The smallest integer with 6 zeros in both decimal and binary expansion is 100007900=101111101011111111111011100b.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 550 terms from Enrique Pérez Herrero)

Example

a(6)=30 because 30 base 2 = 11110 and both terms have the same number of zeros.

Mathematica

Select[Range[0, 20000], DigitCount[#, 10, 0]==DigitCount[#, 2, 0]&] (* Harvey P. Dale, Jun 19 2021 *)

Crossrefs

Cf. A023416, A153115.

Sequence in context: A283606 A147400 A002545 * A325664 A290865 A055795

Adjacent sequences: A153111 A153112 A153113 * A153115 A153116 A153117

Keyword

nonn,base

Author

Gil Broussard, Dec 18 2008

Status

approved