A046500 Smallest prime with multiplicative persistence n.

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

Offset: 0

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• more
• hard
• nice

Comments

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

Examples

			47 -> 28 -> 16 -> 6 has persistence 3.
		

Links

• Shyam Sunder Gupta, Digital Root Wonders, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 1, 1-28.
• Carlos Rivera, Puzzle 22. Primes & Persistence, The Prime Puzzles & Problems Connection.
• N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
• Eric Weisstein's World of Mathematics, Multiplicative Persistence.

Crossrefs

Cf. A003001, A014120.

Programs

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 *)

Extensions

a(10)-a(11) found by Jud McCranie