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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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,25

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]

LINKS

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

EXAMPLE

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

f(32)=3*2=6.

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

CROSSREFS

Cf. A087471, A087473, A087474.

Sequence in context: A143544 A031346 A335808 * A172069 A054348 A239660

Adjacent sequences:  A087469 A087470 A087471 * A087473 A087474 A087475

KEYWORD

nonn,base

AUTHOR

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

STATUS

approved

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)