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A065710
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Number of 2's in the decimal expansion of 2^n.
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20
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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
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0,19
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = a(floor(n/10)) + [n == 2 (mod 10)], where [...] is the Iverson bracket. - M. F. Hasler, Feb 10 2023
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MATHEMATICA
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Table[ Count[ IntegerDigits[2^n], 2], {n, 0, 100} ]
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PROG
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(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, 2); write("b065710.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 26 2009
(PARI) a(n) = #select(x->(x==2), digits(2^n)); \\ Michel Marcus, Jun 15 2018
(Python)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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