A055253 Number of even digits in 2^n.

0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 4, 3, 2, 3, 3, 2, 2, 5, 5, 4, 3, 4, 6, 3, 3, 6, 4, 6, 4, 5, 7, 6, 4, 4, 4, 5, 4, 7, 5, 4, 5, 7, 9, 8, 8, 8, 7, 8, 6, 10, 8, 7, 7, 9, 9, 6, 8, 8, 11, 11, 9, 12, 10, 10, 10, 13, 9, 8, 8, 10, 16, 15, 10, 13, 8, 7, 12, 12, 14, 13, 12, 15, 11, 12, 14, 10, 14, 16, 14, 16

Offset: 0

Author

Asher Auel, May 05 2000

Keywords

• nonn
• base
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A055254, A034887.

Programs

Maple

A055253 := proc(val) local i, j, k, n; n := 2^val; j := 0; k := floor(ln(n)/ln(10))+1; for i from 1 to k do if (n mod 10) mod 2 = 0 then j := j+1 fi; n := floor(n/10); od; RETURN(j); end: seq(A055253(n),n=0..110); # Jaap Spies, Dec 30 2003

Mathematica

Table[Length@ Select[IntegerDigits[2^n], EvenQ], {n, 0, 120}] (* or *)
Table[Total@ Pick[DigitCount[2^n], {0, 1, 0, 1, 0, 1, 0, 1, 0, 1}, 1], {n, 0, 120}] (* Michael De Vlieger, May 01 2016 *)
Count[IntegerDigits[#],?EvenQ]&/@(2^Range[0,100]) (* _Harvey P. Dale, Mar 25 2020 *)

PARI

a(n) = #select(x->(x % 2) == 0, digits(2^n)); \\ Michel Marcus, May 01 2016

Python

def a(n): return sum(1 for d in str(1<Michael S. Branicky, Dec 23 2022

Extensions

More terms from Jaap Spies, Dec 30 2003