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

%I A069535 #10 Apr 28 2021 20:43:43
%S A069535 1,2,4,20,30,33,42,44,45,51,60,67,72,75,78,79,80,81,82,84,88,91,94,95,
%T A069535 97,98,99,116,140,141,166,170,180,188,198,200,202,210,222,228,231,238,
%U A069535 252,261,264,265,272,285,286,292,293,297,311,313,315,317,321
%N A069535 Treated as strings, n and its reversal are substrings of n!.
%C A069535 This is the sequence of "fixated points" (cf. A068588) of f(n) = n!.
%H A069535 Robert Israel, <a href="/A069535/b069535.txt">Table of n, a(n) for n = 1..10000</a>
%H A069535 Pe, J. <a href="http://numeratus.net/enlightened/fixated.html">Fixated Points of Arithmetical Functions</a>
%e A069535 42! = 1405006117752879898543142606244511569936384000000000, which contains both 42 and 24 as substrings. Hence 42 is a term of the sequence.
%p A069535 filter:= proc(n) local m,L,R,LN; uses StringTools;
%p A069535   L:= sprintf("%d",n);
%p A069535   m:= padic:-ordp(n,10);
%p A069535   R:= Reverse(L)[m+1..-1];
%p A069535   LN:= sprintf("%d",n!);
%p A069535   Search(L,LN) > 0 and Search(R,LN) > 0
%p A069535 end proc:
%p A069535 select(filter, [$1..1000]); # _Robert Israel_, Apr 28 2021
%t A069535 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
%Y A069535 Cf. A068588.
%K A069535 base,nonn
%O A069535 1,2
%A A069535 _Joseph L. Pe_, Apr 16 2002
%E A069535 Edited and extended by _Robert G. Wilson v_, Apr 19 2002