A239427 Numbers such that additive and multiplicative persistences coincide.

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, 30, 31, 32, 33, 37, 38, 40, 41, 42, 46, 48, 50, 51, 56, 58, 60, 61, 64, 65, 67, 70, 71, 73, 76, 80, 81, 82, 83, 84, 85, 90, 92, 99, 100, 101, 102, 103, 104, 105, 106

Offset

1,3

Comments

Numbers n for which A031286(n) = A031346(n).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..66 from Arkadiusz Wesolowski)

Eric Weisstein's World of Mathematics, Additive Persistence

Eric Weisstein's World of Mathematics, Multiplicative Persistence

Example

28 -> 10 -> 1 has additive persistence 2. 28 -> 16 -> 6 has multiplicative persistence 2. 28 is therefore in the sequence.

Prog

(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, ", ")));
(Python)
from math import prod
def A031286(n):
    ap = 0
    while n > 9: n, ap = sum(map(int, str(n))), ap+1
    return ap
def A031346(n):
    mp = 0
    while n > 9: n, mp = prod(map(int, str(n))), mp+1
    return mp
def ok(n): return A031286(n) == A031346(n)
print([k for k in range(107) if ok(k)]) # Michael S. Branicky, Sep 17 2022

Crossrefs

Supersequence of A239480. Cf. A031286, A031346, A064702.

Sequence in context: A298639 A276347 A076121 * A255422 A080681 A366186

Adjacent sequences: A239424 A239425 A239426 * A239428 A239429 A239430

Keyword

nonn,base

Author

Arkadiusz Wesolowski, Mar 19 2014

Status

approved