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A064868
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The minimal number which has multiplicative persistence 4 in base n.
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11
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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
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OFFSET
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5,1
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = 5*n-floor(n/24) for n > 23.
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EXAMPLE
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a(6) = 172 because 172 = [444]->[144]->[24]->[12]->[2] and no lesser n has persistence 4 in base 6.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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