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Numbers k such that k is a substring of 2^k.
11

%I #27 Feb 17 2024 10:29:16

%S 6,10,35,36,37,44,49,51,60,67,72,73,82,85,89,93,179,188,190,191,226,

%T 234,252,297,312,321,356,373,391,425,429,430,438,445,451,475,478,479,

%U 486,516,519,521,526,549,551,581,582,583,598,601,603,609,613,619,627,632,642,652,653,655,660

%N Numbers k such that k is a substring of 2^k.

%H David W. Wilson, <a href="/A032740/b032740.txt">Table of n, a(n) for n = 1..10000</a>

%e 2^93 = 99035203142830421991929_93_792.

%t 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 *)

%t Select[Range[700],SequenceCount[IntegerDigits[2^#],IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 10 2019 *)

%o (Haskell)

%o import Data.List (isInfixOf)

%o a032740 n = a032740_list !! (n-1)

%o a032740_list = [x | x <- [0..], show x `isInfixOf` (show $ 2 ^ x)]

%o -- _Reinhard Zumkeller_, Jan 19 2014

%Y Cf. A049301-A049307.

%K base,nonn,nice,easy

%O 1,1

%A _Patrick De Geest_, May 15 1998