A087472 Number of iterations required for the function f(n) to reach a single digit, where f(n) is the product of the two numbers formed from the alternating digits of n.

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

Offset: 1

Author

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

Keywords

• nonn
• base

Comments

A087471(n) gives the final digit reached by successive iterations of Murthy's function, f(n). A087473(n) gives the smallest number that requires n iterations of Murthy's function to reach a single digit. The n-th row of triangle A087474 gives the n successive iterations of Murthy's function on A087473(n).

Differs from A031346 first at n=110. [From R. J. Mathar, Sep 11 2008]

Examples

			a(1234)= 3 since f(1234)=13*24=312, f(312)=32*1=32 and
f(32)=3*2=6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A087471, A087473, A087474.

Programs

Maple

murthy:= proc(n) local L,d;
  L:= convert(n,base,10);
  d:= nops(L);
  add(L[2*i+1]*10^i,i=0..(d-1)/2)*add(L[2*i+2]*10^i,i=0..(d-2)/2)
end proc:
A087472:= proc(n) option remember;
  if n < 10 then  0 else 1+procname(murthy(n)) fi
end proc:
map(A087472, [$1..200]); # Robert Israel, Feb 14 2017