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

Author

Sascha Kurz, Oct 08 2001

Keywords

• base
• easy
• nonn

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.

Examples

			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.
		

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
• Index entries for linear recurrences with constant coefficients, order 721.

Crossrefs

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

Formula

a(n) = 7*n-[n/720] for n > 719.