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

0, 1, 5, 6, 10, 47, 50, 60, 75, 78, 100, 125, 152, 457, 500, 600, 750, 1000, 1025, 1052, 1250, 1520, 5000, 5625, 6000, 7500, 10000, 10025, 10052, 10250, 10520, 12266, 12500, 15200, 23258, 43567, 50000, 56250, 60000, 62656, 75000, 82291, 90625, 98254, 100000, 100025, 100052, 100250, 100520

Offset: 1

Author

Scott R. Shannon, Mar 01 2021

Keywords

• nonn
• base

Comments

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.

Examples

			6 is a term as 6*reverse(6) = 6*6 = 36 contains '6' as a substring.
47 is a term as 47*reverse(47) = 47*74 = 3478 contains '47' as a substring.
1052 is a term as 1052*reverse(1052) = 1052*2501 = 2631052 contains '1052' as a substring.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..153

Crossrefs

Cf. A061205, A342130 (base 2), A001477, A004086, A181721, A203565, A332795.

Programs

Maple

filter:= proc(n) local L,d,Lp,r,i;
  L:= convert(n,base,10);
  d:= nops(L);
  r:= add(L[-i]*10^(i-1),i=1..d);
  Lp:= convert(n*r,base,10);
  ormap(t -> Lp[t..t+d-1] = L, [$1..nops(Lp)+1-d])
end proc:
select(filter, [$0..120000]); # Robert Israel, Mar 24 2024

Mathematica

Select[Range[0,110000],SequenceCount[IntegerDigits[# IntegerReverse[#]],IntegerDigits[#]]>0&] (* Harvey P. Dale, Apr 20 2024 *)

PARI

isok(m) = #strsplit(Str(m*fromdigits(Vecrev(digits(m)))), Str(m)) > 1; \\ Michel Marcus, Mar 01 2021

Python

def ok(n): return (s:=str(n)) in str(n*int(s[::-1]))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Mar 25 2024