A064869 The minimal number which has multiplicative persistence 5 in base n.

244140624, 3629, 1601, 1535, 394, 679, 317, 1099, 127, 135, 582, 187, 168, 157, 201, 159, 230, 215, 180, 185, 246, 181, 188, 195, 198, 323, 239, 255, 259, 267, 239, 287, 295, 293, 310, 313, 280, 377, 375, 395, 347, 360, 321, 370, 439, 431, 458, 355, 362

Offset: 5

Author

Sascha Kurz, Oct 09 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(3) and a(4) seem not to exist.

Examples

			a(9)=394 because 394=[477]->[237]->[46]->[26]->[13]->[3] and no smaller n has persistence 5 in base 9.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 5..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.
• Carlos Rivera, Puzzle 22. Primes and Persistence, The Prime Puzzles and Problems Connection.
• 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 121.

Crossrefs

Cf. A003001, A031346, A064867, A064868, A064870, A064871, A064872.

Formula

a(n) = 6*n-floor(n/120) for n > 119.