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A239427 Numbers such that additive and multiplicative persistences coincide.

%I A239427 #36 Feb 16 2025 08:33:21
%S A239427 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,28,29,
%T A239427 30,31,32,33,37,38,40,41,42,46,48,50,51,56,58,60,61,64,65,67,70,71,73,
%U A239427 76,80,81,82,83,84,85,90,92,99,100,101,102,103,104,105,106
%N A239427 Numbers such that additive and multiplicative persistences coincide.
%C A239427 Numbers n for which A031286(n) = A031346(n).
%H A239427 Michael S. Branicky, <a href="/A239427/b239427.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..66 from Arkadiusz Wesolowski)
%H A239427 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AdditivePersistence.html">Additive Persistence</a>
%H A239427 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%e A239427 28 -> 10 -> 1 has additive persistence 2. 28 -> 16 -> 6 has multiplicative persistence 2. 28 is therefore in the sequence.
%o A239427 (PARI) for(n=0, 106, v=n; a=0; while(n>9, a++; n=sumdigits(n)); n=v; m=0; while(n>9, m++; d=digits(n); n=prod(k=1, #d, d[k])); n=v; if(a==m, print1(n, ", ")));
%o A239427 (Python)
%o A239427 from math import prod
%o A239427 def A031286(n):
%o A239427     ap = 0
%o A239427     while n > 9: n, ap = sum(map(int, str(n))), ap+1
%o A239427     return ap
%o A239427 def A031346(n):
%o A239427     mp = 0
%o A239427     while n > 9: n, mp = prod(map(int, str(n))), mp+1
%o A239427     return mp
%o A239427 def ok(n): return A031286(n) == A031346(n)
%o A239427 print([k for k in range(107) if ok(k)]) # _Michael S. Branicky_, Sep 17 2022
%Y A239427 Supersequence of A239480. Cf. A031286, A031346, A064702.
%K A239427 nonn,base
%O A239427 1,3
%A A239427 _Arkadiusz Wesolowski_, Mar 19 2014