

A046500


Smallest prime with multiplicative persistence n.


11



2, 11, 29, 47, 277, 769, 8867, 186889, 2678789, 26899889, 3778888999, 277777788888989
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OFFSET

0,1


COMMENTS

The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit.


LINKS

Table of n, a(n) for n=0..11.
C. Rivera, Puzzle page
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 9798.
Eric Weisstein's World of Mathematics, Multiplicative Persistence.


EXAMPLE

47 > 28 > 16 > 6 has persistence 3.


MATHEMATICA

a[n_]:=Length[NestWhileList[Times@@IntegerDigits[#]&, n, #>9&]]1; t={}; i=1; Do[While[a[p=Prime[i]]!=n, i++]; AppendTo[t, p], {n, 0, 9}]; t (* Jayanta Basu, Jun 02 2013 *)


CROSSREFS

Cf. A003001, A014120.
Sequence in context: A136317 A090389 A061238 * A062123 A117560 A024178
Adjacent sequences: A046497 A046498 A046499 * A046501 A046502 A046503


KEYWORD

nonn,base,more,hard,nice


AUTHOR

Patrick De Geest, Sep 15 1998


EXTENSIONS

Value for n=10 and n=11 found by Jud McCranie


STATUS

approved



