A046500 - OEIS

%I #24 Mar 10 2025 11:51:02

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

%T 277777788888989

%N Smallest prime with multiplicative persistence n.

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

%H Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_1">Digital Root Wonders</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 1, 1-28.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_022.htm">Puzzle 22. Primes & Persistence</a>, The Prime Puzzles & Problems Connection.

%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/persistence.html">The persistence of a number</a>, J. Recreational Math., 6 (1973), 97-98.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence.</a>

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

%t 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 *)

%Y Cf. A003001, A014120.

%K nonn,base,more,hard,nice,changed

%O 0,1

%A _Patrick De Geest_, Sep 15 1998

%E a(10)-a(11) found by _Jud McCranie_