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A263131 Ordinal transform of the multiplicative persistence A031346.

%I A263131 #12 Feb 16 2025 08:33:27
%S A263131 1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,4,5,
%T A263131 16,17,18,19,6,7,8,9,10,1,20,21,22,11,12,13,14,2,15,3,23,24,16,17,18,
%U A263131 4,19,5,20,6,25,26,21,22,23,24,7,25,8,9,27,28,26,27
%N A263131 Ordinal transform of the multiplicative persistence A031346.
%C A263131 n is the a(n)-th nonnegative integer having its multiplicative persistence.
%H A263131 Alois P. Heinz, <a href="/A263131/b263131.txt">Table of n, a(n) for n = 0..20000</a>
%H A263131 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%F A263131 a(n) = |{ j in {0..n} : A031346(j) = A031346(n) }|.
%p A263131 m:= n-> mul(i, i=convert(n, base, 10)):
%p A263131 p:= n-> `if`(n<10, 0, 1+p(m(n))):
%p A263131 b:= proc() 0 end:
%p A263131 a:= proc(n) option remember; local t;
%p A263131       t:= p(n); b(t):= b(t)+1
%p A263131     end:
%p A263131 seq(a(n), n=0..100);
%Y A263131 Cf. A031346.
%K A263131 nonn,look,base
%O A263131 0,2
%A A263131 _Alois P. Heinz_, Oct 10 2015