A069535 Treated as strings, n and its reversal are substrings of n!.

1, 2, 4, 20, 30, 33, 42, 44, 45, 51, 60, 67, 72, 75, 78, 79, 80, 81, 82, 84, 88, 91, 94, 95, 97, 98, 99, 116, 140, 141, 166, 170, 180, 188, 198, 200, 202, 210, 222, 228, 231, 238, 252, 261, 264, 265, 272, 285, 286, 292, 293, 297, 311, 313, 315, 317, 321

Offset

1,2

Comments

This is the sequence of "fixated points" (cf. A068588) of f(n) = n!.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Pe, J. Fixated Points of Arithmetical Functions

Example

42! = 1405006117752879898543142606244511569936384000000000, which contains both 42 and 24 as substrings. Hence 42 is a term of the sequence.

Maple

filter:= proc(n) local m, L, R, LN; uses StringTools;
  L:= sprintf("%d", n);
  m:= padic:-ordp(n, 10);
  R:= Reverse(L)[m+1..-1];
  LN:= sprintf("%d", n!);
  Search(L, LN) > 0 and Search(R, LN) > 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Apr 28 2021

Mathematica

r = {}; Do[m = n!; s = ToString[m]; If[ StringPosition[s, ToString[n]] != {} && StringPosition[s, ToString[ FromDigits[ Reverse[ IntegerDigits[n]]]]] != {}, r = Append[r, n]], {n, 1, 321}]; r

Crossrefs

Cf. A068588.

Sequence in context: A215815 A295826 A201502 * A108866 A259122 A059206

Adjacent sequences: A069532 A069533 A069534 * A069536 A069537 A069538

Keyword

base,nonn

Author

Joseph L. Pe, Apr 16 2002

Extensions

Edited and extended by Robert G. Wilson v, Apr 19 2002

Status

approved