A065712 Number of 1's in decimal expansion of 2^n.

1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 0, 3, 0, 1, 1, 0, 1, 3, 1, 3, 0, 3, 1, 1, 1, 2, 2, 2, 2, 0, 1, 3, 1, 0, 4, 4, 0, 3, 1, 3, 0, 3, 3, 0, 2, 2, 3, 6, 3, 1, 0, 2, 3, 3, 5, 1, 1, 5, 3, 1, 2, 5, 1, 4, 2, 2, 5, 2, 0, 5, 3, 1, 6, 2, 2, 4, 5, 2

Offset

0,18

Comments

2^17 = 131072 so a(17)=2.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Mathematica

Table[ Count[ IntegerDigits[2^n], 1], {n, 0, 100} ]
Table[DigitCount[2^n, 10, 1], {n, 0, 120}] (* Harvey P. Dale, Aug 15 2014 *)

Prog

(PARI) Count(x, d)= { local(c=0, f); while (x>9, f=x-10*(x\10); if (f==d, c++); x\=10); if (x==d, c++); return(c) }
{ for (n=0, 1000, a=Count(2^n, 1); write("b065712.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 26 2009
(PARI) a(n) = #select(x->(x==1), digits(2^n)); \\ Michel Marcus, Jun 15 2018
(Python)
def A065712(n):
    return str(2**n).count('1') # Chai Wah Wu, Feb 14 2020

Crossrefs

Cf. 0's A027870, 3's A065714, 4's A065715, 5's A065716, 6's A065717, 7's A065718, 8's A065719, 9's A065744.

Sequence in context: A024359 A354512 A088705 * A153172 A242498 A321927

Adjacent sequences: A065709 A065710 A065711 * A065713 A065714 A065715

Keyword

nonn,base

Author

Benoit Cloitre, Dec 04 2001

Extensions

More terms from Robert G. Wilson v, Dec 07 2001

Status

approved