A065710 - OEIS

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A065710

Number of 2's in the decimal expansion of 2^n.

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

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OFFSET

0,19

COMMENTS

2^31 = 2147483648 so a(31) = 1.

See A034293 for indices of zeros: It is conjectured that the last 0 appears at index 168 = A094776(2). More generally, I conjecture that the last occurrence of the term x = 0, 1, 2, 3, ... is at index i = (168, 176, 186, 268, 423, 361, 472, 555, 470, 562, 563, 735, ...). - M. F. Hasler, Feb 10 2023

LINKS

M. F. Hasler, Table of n, a(n) for n = 0..10000 (first 1001 terms from Harry J. Smith), Feb 10 2023

FORMULA

a(n) = a(floor(n/10)) + [n == 2 (mod 10)], where [...] is the Iverson bracket. - M. F. Hasler, Feb 10 2023

MATHEMATICA

Table[ Count[ IntegerDigits[2^n], 2], {n, 0, 100} ]

PROG

(PARI) a(n) = #select(x->(x==2), digits(2^n)); \\ Michel Marcus, Jun 15 2018

(Python)

def A065710(n):

return str(2**n).count('2') # Chai Wah Wu, Feb 14 2020

CROSSREFS