A131809 Multiplicative persistence of Catalan numbers.

0, 0, 0, 0, 1, 1, 1, 3, 1, 5, 4, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,8

Comments

After the 57th terms all the numbers have some digits equal to zero thus the persistence is equal to 1.

Links

Table of n, a(n) for n=0..100.

Example

Catalan number 429 -> 4*2*9=72 -> 7*2=14 -> 1*4=4 thus persistence is 3

Maple

P:=proc(n) local i, k, w, ok, cont; for i from 0 by 1 to n do k:=(2*i)!/(i!*(i+1)!); w:=1; ok:=1; 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);

Crossrefs

Cf. A003001, A006050, A000108.

Sequence in context: A308502 A308674 A308676 * A016574 A210560 A208922

Adjacent sequences: A131806 A131807 A131808 * A131810 A131811 A131812

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 18 2007

Status

approved