A030001 Smallest power of 2 whose decimal expansion contains n.

1024, 1, 2, 32, 4, 256, 16, 32768, 8, 4096, 1024, 1099511627776, 128, 131072, 262144, 2097152, 16, 134217728, 1073741824, 8192, 2048, 262144, 8796093022208, 2199023255552, 1024, 256, 262144, 32768, 128, 4294967296, 4194304, 131072, 32, 33554432, 134217728, 33554432

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice
• look

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A030000 (the exponents), A000079.

Programs

Haskell

import Data.List (isInfixOf)
a030001 n = head $ filter ((show n `isInfixOf`) . show) a000079_list
-- Reinhard Zumkeller, Nov 02 2011

Mathematica

a[n_] := (k = 0; While[ !MatchQ[ IntegerDigits[2^k], {_, Sequence @@ IntegerDigits[n], _}], k++]; 2^k); Table[a[n], {n, 1, 30}](* Jean-François Alcover, Nov 30 2011 *)
Module[{p2=2^Range[0,50]},Table[SelectFirst[p2,SequenceCount[ IntegerDigits[ #], IntegerDigits[ n]]>0&],{n,0,40}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 13 2019 *)

Python

def a(n):
  k, strn = 0, str(n)
  while strn not in str(2**k): k += 1
  return 2**k
print([a(n) for n in range(36)]) # Michael S. Branicky, Apr 03 2024

Extensions

a(30) corrected by Reinhard Zumkeller, Nov 02 2011

a(0) added by N. J. A. Sloane, Jul 04 2017