

A031348


2multiplicative persistence: number of iterations of "multiply 2nd powers of digits" needed to reach 0 or 1.


3



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
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OFFSET

1,2


REFERENCES

M. Gardner, Fractal Music, Hypercards and More Mathematical Recreations from Scientific American, Persistence of Numbers, pp. 1201; 1867, W. H. Freeman, NY, 1992.


LINKS

Table of n, a(n) for n=1..99.
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), 9798.
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


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



