login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049329 Numbers n such that n is a substring of n^n. 8
1, 5, 6, 9, 10, 11, 16, 17, 19, 21, 24, 25, 28, 31, 32, 33, 35, 36, 37, 39, 41, 42, 43, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 59, 60, 61, 63, 64, 66, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 86, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 108, 111, 115 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For typical large n, the string corresponding to n^n has length on the order of n log_10(n); heuristically, each substring of length d = log_10(n) has probability 10^(-d) ~ 1/n of matching n, and the probability that none of these matches is about exp(-log_10(n)) = n^(-log_10(e)) ~ n^(-0.434). Thus we should expect that most large n are in the sequence, but infinitely many are not. - Robert Israel, Jul 14 2015

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

MAPLE

filter:= proc(n) local L, Ln;

L:= convert(n, string);

Ln:= convert(n^n, string);

StringTools:-Search(L, Ln) <> 0

end proc:

select(filter, [$1..1000]); # Robert Israel, Jul 13 2015

MATHEMATICA

ssQ[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[ IntegerDigits[ n^n], Length[idn], 1], idn]]; Select[Range[120], ssQ] (* Harvey P. Dale, Apr 01 2011 *)

CROSSREFS

Sequence in context: A087176 A227006 A139454 * A195925 A284936 A188191

Adjacent sequences:  A049326 A049327 A049328 * A049330 A049331 A049332

KEYWORD

base,nonn,easy,nice

AUTHOR

David W. Wilson

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 10:48 EST 2017. Contains 294963 sequences.