The On-Line Encyclopedia of Integer Sequences (OEIS)

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A175394

Least nontrivial exponent e > 2 such that n^2 is a substring of n^e (n >= 0).
(history; published version)

#9 by Bruno Berselli at Wed Mar 21 04:34:54 EDT 2018

STATUS

proposed

approved

#8 by Jon E. Schoenfield at Tue Mar 20 23:00:23 EDT 2018

STATUS

editing

proposed

#7 by Jon E. Schoenfield at Tue Mar 20 23:00:20 EDT 2018

NAME

Least nontrivial exponent e > 2 such that n^2 is a substring of n^e (n >= 0).

STATUS

proposed

editing

#6 by Robert Israel at Tue Mar 20 22:45:25 EDT 2018

STATUS

editing

proposed

#5 by Robert Israel at Tue Mar 20 22:43:47 EDT 2018

LINKS

Robert Israel, <a href="/A175394/b175394.txt">Table of n, a(n) for n = 0..2000</a>

MAPLE

f:= proc(n) local pat, e;

pat:= sprintf("%d", n^2);

for e from 3 do if StringTools:-Search(pat, sprintf("%d", n^e))<> 0 then return e fi od:

end proc:

map(f, [$0..100]); # Robert Israel, Mar 20 2018

STATUS

approved

editing

#4 by Harvey P. Dale at Sat Aug 17 17:15:34 EDT 2013

STATUS

editing

approved

#3 by Harvey P. Dale at Sat Aug 17 17:15:29 EDT 2013

MATHEMATICA

lne[n_]:=Module[{e=3, idn2=IntegerDigits[n^2]}, While[!MemberQ[ Partition[ IntegerDigits[n^e], Length[ idn2], 1], idn2], e++]; e]; Array[lne, 70, 0] (* Harvey P. Dale, Aug 17 2013 *)

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:26:32 EDT 2012

AUTHOR

_Zak Seidov (zakseidov(AT)yahoo.com), _, Apr 29 2010

Discussion

Fri Mar 30

17:26

OEIS Server: https://oeis.org/edit/global/139

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Least nontrivial exponent e>2 such that n^2 is a substring of n^e (n>=0).

DATA

3, 3, 6, 6, 7, 3, 7, 6, 22, 11, 3, 13, 26, 54, 123, 27, 27, 40, 100, 43, 6, 43, 54, 42, 12, 3, 37, 43, 9, 37, 6, 19, 102, 102, 43, 96, 83, 45, 67, 34, 12, 128, 168, 102, 182, 44, 152, 104, 184, 52, 3, 17, 35, 75, 164, 67, 127, 22, 134, 98, 7, 124, 117, 146, 77, 146, 156, 87

OFFSET

0,1

EXAMPLE

a(2)=6 because 2^2=4 is a substring of 2^6=64

a(4)=7 because 4^2=16 is a substring of 4^7=16384.

CROSSREFS

Cf. A008856, A033819, A045537, A074250.

KEYWORD

base,nonn,new

AUTHOR

Zak Seidov (zakseidov(AT)yahoo.com), Apr 29 2010

STATUS

approved