A064872 The minimal number which has multiplicative persistence 8 in base n.

7577, 130883, 596667, 3644381, 2820, 61773, 2752, 5136, 7452, 38631, 2780, 8015, 2996, 542, 8611, 4591, 575, 10586, 2532, 2681, 2764, 1016, 4547, 10151, 1065, 983, 813, 5431, 900, 1255, 983, 5179, 5117, 1190, 982, 1129, 1501, 1491, 1471, 1084

Offset: 13

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(7)=1086400325525346, a(10)=2677889, a(11)=757074, a(8) and a(9) seem not to exist.

Examples

			a(13) = 7577 because 7577 is the fewest number with persistence 8 in base 13.
		

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.
• 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 40321.

Crossrefs

Cf. A003001, A031346, A064867, A064868, A064869, A064870, A064871.

Formula

a(n) = 9*n-[n/40320] for n > 40319.