A064870 The minimal number which has multiplicative persistence 6 in base n.

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

Michael De Vlieger, Table of n, a(n) for n = 7..10000

M. R. Diamond and D. D. Reidpath, A counterexample to a conjecture of Sloane and Erdos, J. Recreational Math., 1998 29(2), 89-92.

Sascha Kurz, Persistence in different bases

T. Lamont-Smith, Multiplicative Persistence and Absolute Multiplicative Persistence, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.

C. Rivera, Minimal prime with persistence p

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.

Crossrefs

Cf. A003001, A031346, A064867, A064868, A064869, A064871, A064872.

Sequence in context: A237171 A246248 A031630 * A051520 A051346 A217125

Adjacent sequences: A064867 A064868 A064869 * A064871 A064872 A064873

Keyword

base,easy,nonn

Author

Sascha Kurz, Oct 08 2001

Status

approved