A046510 Numbers with multiplicative persistence value 1.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30, 31, 32, 33, 40, 41, 42, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 130, 131, 132, 133

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Comments

Numbers 0 to 9 have a multiplication persistence of 0, not 1. - Daniel Mondot, Mar 12 2022

Examples

			24 -> 2 * 4 = [ 8 ] -> one digit in one step.
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
• Eric Weisstein's World of Mathematics, Multiplicative Persistence

Crossrefs

Cf. A003001, A014120, A046501.

Numbers with multiplicative persistence m: this sequence (m=1), A046511 (m=2), A046512 (m=3), A046513 (m=4), A046514 (m=5), A046515 (m=6), A046516 (m=7), A046517 (m=8), A046518 (m=9), A352531 (m=10), A352532 (m=11).

Programs

Mathematica

Select[Range[10, 121], IntegerLength[Times @@ IntegerDigits[#]] <= 1 &] (* Jayanta Basu, Jun 26 2013 *)

PARI

isok(n) = my(d=digits(n)); (#d > 1) && (#digits(prod(k=1, #d, d[k])) <= 1); \\ Michel Marcus, Apr 12 2018 and Mar 13 2022

Python

from math import prod
def ok(n): return n > 9 and prod(map(int, str(n))) < 10
print([k for k in range(134) if ok(k)]) # Michael S. Branicky, Mar 13 2022

Extensions

Incorrect terms 0 to 9 removed by Daniel Mondot, Mar 12 2022