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