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A064870
The minimal number which has multiplicative persistence 6 in base n.
8
11262, 57596799, 30536, 6788, 4684, 1571, 439, 667, 1964, 683, 218, 857, 264, 278, 353, 393, 227, 382, 344, 311, 319, 307, 283, 417, 422, 381, 485, 436, 349, 431, 436, 449, 421, 469, 327, 575, 598, 483, 539, 413, 511, 517, 534, 641, 611, 609, 476, 479
OFFSET
7,1
COMMENTS
The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(5)=1811981201171874, a(6) seems not to exist.
LINKS
M. R. Diamond and D. D. Reidpath, A counterexample to a conjecture of Sloane and Erdos, J. Recreational Math., 1998 29(2), 89-92.
T. Lamont-Smith, Multiplicative Persistence and Absolute Multiplicative Persistence, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Multiplicative Persistence
FORMULA
a(n) = 7*n-[n/720] for n > 719.
EXAMPLE
a(13) = 439 because 439 = [2'7'10]->[10'10]->[7'9]->[4'11]->[3'5]->[1'2]->[2] needs 6 steps and no fewer n.
KEYWORD
base,easy,nonn
AUTHOR
Sascha Kurz, Oct 08 2001
STATUS
approved