A046500 Smallest prime with multiplicative persistence n.

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

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), 97-98.

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 A345213 A117560

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