A032740 Numbers k such that k is a substring of 2^k.

6, 10, 35, 36, 37, 44, 49, 51, 60, 67, 72, 73, 82, 85, 89, 93, 179, 188, 190, 191, 226, 234, 252, 297, 312, 321, 356, 373, 391, 425, 429, 430, 438, 445, 451, 475, 478, 479, 486, 516, 519, 521, 526, 549, 551, 581, 582, 583, 598, 601, 603, 609, 613, 619, 627, 632, 642, 652, 653, 655, 660

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• base
• nonn
• nice
• easy

Examples

			2^93 = 99035203142830421991929_93_792.
		

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A049301, A049302, A049303, A049304, A049305, A049306, A049307.

Programs

Haskell

import Data.List (isInfixOf)
a032740 n = a032740_list !! (n-1)
a032740_list = [x | x <- [0..], show x `isInfixOf` (show $ 2 ^ x)]
-- Reinhard Zumkeller, Jan 19 2014

Mathematica

d[n_] := IntegerDigits[n]; parQ[n_] := MemberQ[Partition[d[2^n], Length[x = d[n]], 1], x]; Select[Range[660], parQ] (* Jayanta Basu, Jun 17 2013 *)
Select[Range[700],SequenceCount[IntegerDigits[2^#],IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 10 2019 *)