A263131 Ordinal transform of the multiplicative persistence A031346.

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, 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, 4, 19, 5, 20, 6, 25, 26, 21, 22, 23, 24, 7, 25, 8, 9, 27, 28, 26, 27

Offset: 0

Author

Alois P. Heinz, Oct 10 2015

Keywords

• nonn
• look
• base

Comments

n is the a(n)-th nonnegative integer having its multiplicative persistence.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000
• Eric Weisstein's World of Mathematics, Multiplicative Persistence

Crossrefs

Cf. A031346.

Programs

Maple

m:= n-> mul(i, i=convert(n, base, 10)):
p:= n-> `if`(n<10, 0, 1+p(m(n))):
b:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= p(n); b(t):= b(t)+1
    end:
seq(a(n), n=0..100);

Formula

a(n) = |{ j in {0..n} : A031346(j) = A031346(n) }|.