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A064867
The minimal number which has multiplicative persistence 3 in base n.
11
26, 63, 68, 23, 27, 31, 35, 39, 43, 46, 50, 54, 58, 62, 66, 69, 73, 77, 81, 85, 89, 92, 96, 100, 104, 108, 112, 115, 119, 123, 127, 131, 135, 138, 142, 146, 150, 154, 158, 161, 165, 169, 173, 177, 181, 184, 188, 192
OFFSET
3,1
COMMENTS
The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit.
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) = 4*n-floor(n/6) for n > 5.
EXAMPLE
a(3) = 26 because 26 = [222]->[22]->[11]->[1] and no fewer n has persistence 3 in base 3.
MATHEMATICA
With[{m = 3}, Table[Block[{k = 1}, While[Length@ FixedPointList[Times @@ IntegerDigits[#, n] &, k, 100] != m + 2, k++]; k], {n, 3, 5}]]~Join~Array[4 # - Floor[#/6] &, 45, 6] (* Michael De Vlieger, Aug 30 2021 *)
KEYWORD
base,easy,nonn
AUTHOR
Sascha Kurz, Oct 08 2001
STATUS
approved