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A064868
The minimal number which has multiplicative persistence 4 in base n.
11
2344, 172, 131, 174, 52, 77, 75, 83, 75, 81, 89, 95, 101, 104, 110, 133, 143, 127, 133, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283
OFFSET
5,1
COMMENTS
The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(3) and a(4) do not seem to exist.
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.
T. Lamont-Smith, Multiplicative Persistence and Absolute Multiplicative Persistence, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
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) = 5*n-floor(n/24) for n > 23.
EXAMPLE
a(6) = 172 because 172 = [444]->[144]->[24]->[12]->[2] and no lesser n has persistence 4 in base 6.
MATHEMATICA
With[{m = 4, r = 24}, Table[Block[{k = 1}, While[Length@ FixedPointList[Times @@ IntegerDigits[#, n] &, k] != m + 2, k++]; k], {n, m + 1, r}]~Join~Array[(m + 1) # - Floor[#/r] &, 34, r + 1]] (* Michael De Vlieger, Aug 30 2021 *)
PROG
(PARI) pers(nn, b) = {ok = 0; p = 0; until (ok, d = digits(nn, b); if (#d == 1, ok = 1, p++); nn = prod(k=1, #d, d[k]); if (nn == 0, ok = 1); ); return (p); }
a(n) = {i=0; while (pers(i, n) != 4, i++); return (i); } \\ Michel Marcus, Jun 30 2013
KEYWORD
base,easy,nonn
AUTHOR
Sascha Kurz, Oct 09 2001
EXTENSIONS
Example modified by Harvey P. Dale, Oct 19 2022
STATUS
approved