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

Author

Gil Broussard, Dec 18 2008

Keywords

• nonn
• base

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.

Examples

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

Links

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

Crossrefs

Cf. A023416, A153115.

Programs

Mathematica

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