A030000 a(n) is the smallest nonnegative number k such that the decimal expansion of 2^k contains the string n.
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
Offset: 0
Examples
2^12 = 4096 is first power of 2 containing a 9, so a(9) = 12.
Links
- Giovanni Resta, Table of n, a(n) for n = 0..10000 (terms up to a(1000) from T. D. Noe, a(9634) corrected by Piotr Idzik)
Crossrefs
Programs
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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 -- Reinhard Zumkeller, Aug 04 2011
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Mathematica
Table[ i=0; While[ StringPosition[ ToString[ 2^i ], ToString[ n ] ]=={}, i++ ]; i, {n, 0, 80} ] snn[n_]:=Module[{k=0},While[SequenceCount[IntegerDigits[2^k],IntegerDigits[n]]==0,k++];k]; Array[snn,100,0] (* Harvey P. Dale, Mar 16 2025 *) -
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
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Python
def a(n): k, strn = 0, str(n) while strn not in str(2**k): k += 1 return k print([a(n) for n in range(74)]) # Michael S. Branicky, Mar 06 2021
Formula
a(n) <= A018856(n) for n >= 1. - Pontus von Brömssen, Jul 21 2021
Extensions
More terms from Hans Havermann
Comments