A350836 Numbers k such that A103168(k) = A340592(k).

1, 2, 3, 5, 7, 11, 14, 50, 101, 131, 151, 181, 191, 194, 313, 353, 373, 383, 712, 727, 757, 762, 787, 797, 919, 929, 1100, 1994, 2701, 4959, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 17 2022

Keywords

• nonn
• base

Comments

Numbers k such that the concatenation of the prime factors of k with multiplicity is congruent mod k to the reverse of k.

Terms for which the common value of A103168(k) and A340592(k) is prime include 14, 50, 194, 1100, and 116416.

Examples

			a(7) = 14 is a term because A103168(14) = 41 mod 14 = 13 and A340592(14) = 27 mod 14 = 13.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2200

Crossrefs

Includes A002385. Cf. A004086, A037276, A103168, A340592.

Programs

Maple

revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
f:= proc(n) local L,p,i,r;
  L:= sort(map(t -> t[1]$t[2],ifactors(n)[2]));
  r:= L[1];
  for i from 2 to nops(L) do r:= r*10^(1+max(0,ilog10(L[i])))+L[i] od;
  r
end proc:
f(1):= 1:
select(n -> (f(n) - revdigs(n)) mod n = 0, [$1..20000]);

Python

from sympy import factorint
def A103168(n):
    return int(str(n)[::-1])%n
def A340592(n):
    if n == 1: return 0
    return int("".join(str(f) for f in factorint(n, multiple=True)))%n
def ok(n):
    return A103168(n) == A340592(n)
print([k for k in range(1, 20000) if ok(k)]) # Michael S. Branicky, Jan 18 2022