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

13,1

Comments

The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(7)=1086400325525346, a(10)=2677889, a(11)=757074, a(8) and a(9) seem not to exist.

Links

Table of n, a(n) for n=13..52.

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

Example

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

Crossrefs

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

Sequence in context: A206672 A205516 A260036 * A254909 A254902 A257204

Adjacent sequences: A064869 A064870 A064871 * A064873 A064874 A064875

Keyword

base,easy,nonn

Author

Sascha Kurz, Oct 08 2001

Status

approved