A380759 Number of coincident digits occurring in expression of integers in both base 2 and base 10.

1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3

Offset

1,10

Comments

Multiple occurrences (e.g., two ones) count as two occurrences.

The first term having n occurrences is a(10^(n-1)).

Links

Table of n, a(n) for n=1..100.

Example

a(10) = 2, because 10 in base 10 is 1010 in base 2 (coincident digits 1 and 0).
For n=1002, the following a(1002) = 3 digits coincide,
   n = decimal    1002
   n = binary     1111101010
                         ^^^ same digits

Mathematica

a[n_] := Total[Min /@ Transpose[(DigitCount[n, #, {0, 1}] & /@ {2, 10})]]; Array[a, 100] (* Amiram Eldar, Feb 04 2025 *)

Prog

(PARI) a(n) = my(b=binary(n), d=digits(n)); min(#select(x->(x==1), b), #select(x->(x==1), d)) + min(#select(x->(x==0), b), #select(x->(x==0), d)); \\ Michel Marcus, Feb 04 2025

Crossrefs

Cf. A000027, A007088.

Sequence in context: A332029 A211312 A085978 * A141044 A064284 A371807

Adjacent sequences: A380756 A380757 A380758 * A380760 A380761 A380762

Keyword

nonn,easy,base

Author

Paul Duckett, Feb 01 2025

Extensions

More terms from Michel Marcus, Feb 28 2025

Status

approved