cp's OEIS Frontend

A342127 Numbers m such that the product of m and the string m in reverse contains m as a substring.

%I A342127 #43 Apr 20 2024 11:27:52
%S A342127 0,1,5,6,10,47,50,60,75,78,100,125,152,457,500,600,750,1000,1025,1052,
%T A342127 1250,1520,5000,5625,6000,7500,10000,10025,10052,10250,10520,12266,
%U A342127 12500,15200,23258,43567,50000,56250,60000,62656,75000,82291,90625,98254,100000,100025,100052,100250,100520
%N A342127 Numbers m such that the product of m and the string m in reverse contains m as a substring.
%C A342127 Numerous patterns exist in the terms, e.g., all numbers of the form 1*10^k, 5*10^k, 6*10^k, 75*10^k, 10^(k+2)+25, where k>=0, are in the sequence.
%H A342127 Robert Israel, <a href="/A342127/b342127.txt">Table of n, a(n) for n = 1..153</a>
%e A342127 6 is a term as 6*reverse(6) = 6*6 = 36 contains '6' as a substring.
%e A342127 47 is a term as 47*reverse(47) = 47*74 = 3478 contains '47' as a substring.
%e A342127 1052 is a term as 1052*reverse(1052) = 1052*2501 = 2631052 contains '1052' as a substring.
%p A342127 filter:= proc(n) local L,d,Lp,r,i;
%p A342127   L:= convert(n,base,10);
%p A342127   d:= nops(L);
%p A342127   r:= add(L[-i]*10^(i-1),i=1..d);
%p A342127   Lp:= convert(n*r,base,10);
%p A342127   ormap(t -> Lp[t..t+d-1] = L, [$1..nops(Lp)+1-d])
%p A342127 end proc:
%p A342127 select(filter, [$0..120000]); # _Robert Israel_, Mar 24 2024
%t A342127 Select[Range[0,110000],SequenceCount[IntegerDigits[# IntegerReverse[#]],IntegerDigits[#]]>0&] (* _Harvey P. Dale_, Apr 20 2024 *)
%o A342127 (PARI) isok(m) = #strsplit(Str(m*fromdigits(Vecrev(digits(m)))), Str(m)) > 1; \\ _Michel Marcus_, Mar 01 2021
%o A342127 (Python)
%o A342127 def ok(n): return (s:=str(n)) in str(n*int(s[::-1]))
%o A342127 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Mar 25 2024
%Y A342127 Cf. A061205, A342130 (base 2), A001477, A004086, A181721, A203565, A332795.
%K A342127 nonn,base
%O A342127 1,3
%A A342127 _Scott R. Shannon_, Mar 01 2021