A046510 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

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).

Sequence in context: A102494 A117884 A133506 * A174140 A357929 A322322

Adjacent sequences: A046507 A046508 A046509 * A046511 A046512 A046513

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Sep 15 1998

EXTENSIONS

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

STATUS

approved