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

%I A350836 #11 Jan 24 2022 16:04:59
%S A350836 1,2,3,5,7,11,14,50,101,131,151,181,191,194,313,353,373,383,712,727,
%T A350836 757,762,787,797,919,929,1100,1994,2701,4959,10301,10501,10601,11311,
%U A350836 11411,12421,12721,12821,13331,13831,13931,14341,14741,15451,15551,16061,16361,16561,16661,17471,17971,18181
%N A350836 Numbers k such that A103168(k) = A340592(k).
%C A350836 Numbers k such that the concatenation of the prime factors of k with multiplicity is congruent mod k to the reverse of k.
%C A350836 Terms for which the common value of A103168(k) and A340592(k) is prime include 14, 50, 194, 1100, and 116416.
%H A350836 Robert Israel, <a href="/A350836/b350836.txt">Table of n, a(n) for n = 1..2200</a>
%e A350836 a(7) = 14 is a term because A103168(14) = 41 mod 14 = 13 and A340592(14) = 27 mod 14 = 13.
%p A350836 revdigs:= proc(n) local L,i;
%p A350836   L:= convert(n,base,10);
%p A350836   add(L[-i]*10^(i-1),i=1..nops(L))
%p A350836 end proc:
%p A350836 f:= proc(n) local L,p,i,r;
%p A350836   L:= sort(map(t -> t[1]$t[2],ifactors(n)[2]));
%p A350836   r:= L[1];
%p A350836   for i from 2 to nops(L) do r:= r*10^(1+max(0,ilog10(L[i])))+L[i] od;
%p A350836   r
%p A350836 end proc:
%p A350836 f(1):= 1:
%p A350836 select(n -> (f(n) - revdigs(n)) mod n = 0, [$1..20000]);
%o A350836 (Python)
%o A350836 from sympy import factorint
%o A350836 def A103168(n):
%o A350836     return int(str(n)[::-1])%n
%o A350836 def A340592(n):
%o A350836     if n == 1: return 0
%o A350836     return int("".join(str(f) for f in factorint(n, multiple=True)))%n
%o A350836 def ok(n):
%o A350836     return A103168(n) == A340592(n)
%o A350836 print([k for k in range(1, 20000) if ok(k)]) # _Michael S. Branicky_, Jan 18 2022
%Y A350836 Includes A002385. Cf. A004086, A037276, A103168, A340592.
%K A350836 nonn,base
%O A350836 1,2
%A A350836 _J. M. Bergot_ and _Robert Israel_, Jan 17 2022