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A046510
Numbers with multiplicative persistence value 1.
11
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
1,1
COMMENTS
Numbers 0 to 9 have a multiplication persistence of 0, not 1. - Daniel Mondot, Mar 12 2022
LINKS
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
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
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