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A031348 2-multiplicative persistence: number of iterations of "multiply 2nd powers of digits" needed to reach 0 or 1. 4
0, 7, 6, 6, 3, 5, 5, 4, 5, 1, 1, 7, 6, 6, 3, 5, 5, 4, 5, 1, 7, 6, 5, 4, 2, 4, 5, 3, 4, 1, 6, 5, 5, 4, 3, 4, 4, 3, 4, 1, 6, 4, 4, 3, 2, 3, 3, 2, 4, 1, 3, 2, 3, 2, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 2, 4, 5, 2, 4, 1, 5, 5, 4, 3, 3, 5, 2, 5, 4, 1, 4, 3, 3, 2, 2, 2, 5, 2, 3, 1, 5, 4, 4, 4, 2, 4, 4, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Gardner, Fractal Music, Hypercards and More Mathematical Recreations from Scientific American, Persistence of Numbers, pp. 120-1; 186-7, W. H. Freeman, NY, 1992.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

M. R. Diamond, Multiplicative persistence base 10: some new null results.

N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.

Eric Weisstein's World of Mathematics, Multiplicative Persistence

EXAMPLE

a(14) = 6 because

14 -> 1^2 * 4^2 = 16;

16 -> 1^2 * 6^2 = 36;

36 -> 3^2 * 6^2 = 324;

324 -> 3^2 * 2^2 * 4^2 = 576;

576 -> 5^2 * 7^2 * 6^2 = 44100;

44100 -> 0 => the trajectory is 14 -> 16 -> 36 -> 324 -> 576 -> 44100 -> 0 with 6 iterations. - Michel Lagneau, May 22 2013

MATHEMATICA

m2pd[n_]:=Length[NestWhileList[Times@@(IntegerDigits[#]^2)&, n, #>1&]]-1; Array[m2pd, 100] (* Harvey P. Dale, Apr 19 2020 *)

PROG

(PARI) f(n) = my(d=digits(n)); prod(k=1, #d, d[k]^2);

a(n) = if (n==1, 0, my(nb=1); while(((new = f(n)) > 1), n = new; nb++); nb); \\ Michel Marcus, Jun 13 2018

CROSSREFS

Cf. A031346.

Sequence in context: A188736 A265304 A102769 * A247674 A109696 A257233

Adjacent sequences:  A031345 A031346 A031347 * A031349 A031350 A031351

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified May 26 09:37 EDT 2020. Contains 334620 sequences. (Running on oeis4.)