A129985 - OEIS

A129985

Multiplicative persistence of the prime numbers.

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 3, 1, 2, 1, 2, 3, 2, 3, 3, 1, 1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 3, 2, 2, 2, 3, 1, 1, 3, 3, 2, 1, 2, 3, 3, 2, 3, 1, 2, 2, 3, 2, 2, 4, 2, 3, 3, 1, 1, 1, 2, 1, 3, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 1, 1, 3, 1, 2, 3, 2, 3, 3, 2, 2, 3, 4, 3, 3, 3, 3, 1, 1, 2, 2, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,10

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A031346(A000040(n)). - Alois P. Heinz, Feb 03 2025

EXAMPLE

229 = prime(50) -> 2*2*9 = 36 -> 3*6 = 18 -> 1*8 = 8 -> persistence(229) = 3 = a(50).

MAPLE

P:=proc(n) local i, k, w, ok, cont, x; for i from 1 by 1 to n do k:=ithprime(i); w:=1; ok:=1; x:=k; if k<10 then print(0); else cont:=1; while ok=1 do while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w<10 then ok:=0; print(cont); else cont:=cont+1; k:=w; w:=1; fi; od; fi; od; end: P(100);

MATHEMATICA

s={}; Do[i=0; m=Prime[n]; While[m!=Times@@IntegerDigits[m], m=Times@@IntegerDigits[m]; i++]; AppendTo[s, i], {n, 100}]; s (* James C. McMahon, Feb 03 2025 *)

CROSSREFS

Cf. A000040, A031346.

Sequence in context: A209315 A352218 A174713 * A085243 A372555 A265745

Adjacent sequences: A129982 A129983 A129984 * A129986 A129987 A129988

KEYWORD

easy,nonn,base

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Jun 14 2007

EXTENSIONS

Offset corrected by Alois P. Heinz, Feb 03 2025

STATUS

approved