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Integers with the same number of zeros in base 10 and base 2.
3

%I #15 Jun 19 2021 17:58:29

%S 0,1,3,7,15,30,31,63,127,255,503,507,509,510,511,1003,1005,1006,1015,

%T 1019,1020,1021,1022,2007,2015,2030,2031,2039,2043,2045,2046,3007,

%U 3070,3071,4030,4031,4063,4079,4087,4090,4091,4093,4094,8063,8190,8191,16383

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

%C 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.

%H Giovanni Resta, <a href="/A153114/b153114.txt">Table of n, a(n) for n = 1..10000</a> (first 550 terms from Enrique PĂ©rez Herrero)

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

%t Select[Range[0,20000],DigitCount[#,10,0]==DigitCount[#,2,0]&] (* _Harvey P. Dale_, Jun 19 2021 *)

%Y Cf. A023416, A153115.

%K nonn,base

%O 1,3

%A _Gil Broussard_, Dec 18 2008