A236322 - OEIS

A236322

Number of (potentially overlapping) occurrences of n in the decimal representation of n^n.

1, 0, 0, 0, 1, 3, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 0, 2, 2, 2, 0, 3, 1, 1, 0, 1, 0, 1, 1, 1, 0, 3, 1, 0, 1, 1, 1, 1, 2, 2, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 1, 2, 5, 2, 1, 2, 0, 3, 3, 2, 1, 0, 1, 0, 0, 0, 0, 5, 1, 3, 4, 2, 2, 1, 1, 10

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OFFSET

1,6

COMMENTS

Differs from A236314 at n=99.

LINKS

Scott R. Shannon, Table of n, a(n) for n = 1..10000 (terms 1..999 from Christian Perfect).

MATHEMATICA

a[n_] := Length[StringPosition @@ ToString /@ {n^n, n}]; Array[a, 99] (* Giovanni Resta, Jan 22 2014 *)

PROG

(Python)

from itertools import count

def occurrences(string, sub):

....count = start = 0

....while True:

........start = string.find(sub, start) + 1

........if start > 0:

............count+=1

........else:

............return count

def a(n):

....return occurrences(str(n**n), str(n))

(PARI) a(n) = my(m=Mod(n, 10^#Str(n))); (m==n=n^n)+sum(i=0, 1+log(n)/log(10), m==n\=10) \\ - M. F. Hasler, Jan 23 2014

CROSSREFS

A049329 lists n where a(n) is nonzero.

Non-overlapping occurrences are counted by A236314.

Sequence in context: A262262 A079275 A236314 * A319419 A133574 A133573

Adjacent sequences: A236319 A236320 A236321 * A236323 A236324 A236325

KEYWORD

base,nonn

AUTHOR

Christian Perfect, Jan 22 2014

STATUS

approved