A064871 The minimal number which has multiplicative persistence 7 in base n.

1409794, 68889, 38200, 17902874277, 1494, 2532, 19526, 15838, 1101, 15820, 943, 2674, 2118, 3275, 412, 3310, 1593, 440, 478, 2036, 456, 713, 738, 633, 658, 705, 907, 643, 803, 641, 653, 797, 484, 991, 814, 877, 1079, 767, 840, 575, 930, 843, 710, 880

Offset

9,1

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) = 686285, a(8) seems not to exist.

Links

Table of n, a(n) for n=9..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

Index entries for linear recurrences with constant coefficients, order 5041.

Formula

a(n) = 8*n-[n/5040] for n > 5039.

Example

a(9) = 1409794 because the persistence of 1409794 is 7.

Crossrefs

Cf. A003001, A031346, A064867, A064868, A064869, A064870, A064872.

Sequence in context: A203883 A352611 A337916 * A237397 A301557 A186837

Adjacent sequences: A064868 A064869 A064870 * A064872 A064873 A064874

Keyword

base,easy,nonn

Author

Sascha Kurz, Oct 08 2001

Extensions

Corrected by R. J. Mathar, Nov 02 2007

Status

approved