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Numbers k such that A103168(k) = A340592(k).
2

%I #11 Jan 24 2022 16:04:59

%S 1,2,3,5,7,11,14,50,101,131,151,181,191,194,313,353,373,383,712,727,

%T 757,762,787,797,919,929,1100,1994,2701,4959,10301,10501,10601,11311,

%U 11411,12421,12721,12821,13331,13831,13931,14341,14741,15451,15551,16061,16361,16561,16661,17471,17971,18181

%N Numbers k such that A103168(k) = A340592(k).

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

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

%H Robert Israel, <a href="/A350836/b350836.txt">Table of n, a(n) for n = 1..2200</a>

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

%p revdigs:= proc(n) local L,i;

%p L:= convert(n,base,10);

%p add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p f:= proc(n) local L,p,i,r;

%p L:= sort(map(t -> t[1]$t[2],ifactors(n)[2]));

%p r:= L[1];

%p for i from 2 to nops(L) do r:= r*10^(1+max(0,ilog10(L[i])))+L[i] od;

%p r

%p end proc:

%p f(1):= 1:

%p select(n -> (f(n) - revdigs(n)) mod n = 0, [$1..20000]);

%o (Python)

%o from sympy import factorint

%o def A103168(n):

%o return int(str(n)[::-1])%n

%o def A340592(n):

%o if n == 1: return 0

%o return int("".join(str(f) for f in factorint(n, multiple=True)))%n

%o def ok(n):

%o return A103168(n) == A340592(n)

%o print([k for k in range(1, 20000) if ok(k)]) # _Michael S. Branicky_, Jan 18 2022

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

%K nonn,base

%O 1,2

%A _J. M. Bergot_ and _Robert Israel_, Jan 17 2022