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A030000
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a(n) is the smallest nonnegative number k such that the decimal expansion of 2^k contains the string n.
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24
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10, 0, 1, 5, 2, 8, 4, 15, 3, 12, 10, 40, 7, 17, 18, 21, 4, 27, 30, 13, 11, 18, 43, 41, 10, 8, 18, 15, 7, 32, 22, 17, 5, 25, 27, 25, 16, 30, 14, 42, 12, 22, 19, 22, 18, 28, 42, 31, 11, 32, 52, 9, 19, 16, 25, 16, 8, 20, 33, 33, 23, 58, 18, 14, 6, 16, 46, 24, 15, 34, 29, 21, 17, 30
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listen;
history;
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OFFSET
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0,1
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COMMENTS
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a(n) is well-defined for all n, because 2^k can actually start with (not just contain) any finite sequence of digits without leading zeros. This follows from the facts that log_10(2) is irrational and that the set of fractional parts of n*x is dense in [0,1] if x is irrational. - Pontus von Brömssen, Jul 21 2021
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LINKS
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FORMULA
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EXAMPLE
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2^12 = 4096 is first power of 2 containing a 9, so a(9) = 12.
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MATHEMATICA
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Table[ i=0; While[ StringPosition[ ToString[ 2^i ], ToString[ n ] ]=={}, i++ ]; i, {n, 0, 80} ]
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PROG
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(Haskell)
import Data.List (isInfixOf, findIndex)
import Data.Maybe (fromJust)
a030000 n =
fromJust $ findIndex (show n `isInfixOf`) $ map show a000079_list
(PARI) a(n) = {if (n==1, return (0)); my(k=1, sn = Str(n)); while (#strsplit(Str(2^k), sn) == 1, k++); k; } \\ Michel Marcus, Mar 06 2021
(PARI) apply( A030000(n)={n=Str(n); for(k=0, oo, #strsplit(Str(2^k), n)>1&& return(k))}, [0..99]) \\ Also allows to search for digit strings with leading zeros, e.g., "00" => k=53. - M. F. Hasler, Jul 11 2021
(Python)
def a(n):
k, strn = 0, str(n)
while strn not in str(2**k): k += 1
return k
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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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