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A087473 Smallest positive number that requires n iterations of f(k) to reach a single digit, where f(k) is the product of the two numbers formed from the alternating digits of k. 5
1, 10, 25, 39, 77, 171, 199, 577, 887, 1592, 2682, 3988, 6913, 18747, 39577, 58439, 99428, 173442, 267343, 299137, 574182, 685812, 880543, 1635812, 1974447, 2771717, 18871813, 45797337, 49899368, 58935768, 158504329, 265956179, 566800111, 896125563 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Giovanni Resta, Table of n, a(n) for n = 0..40

EXAMPLE

a(4)= 77 since 77 is the smallest number that requires 4 iterations to reach a single digit: f(77)=7*7=49, f(49)=4*9=36, f(36)=3*6=18, f(18)=1*8=8.

MAPLE

P:=proc(q) local a, b, k, n, t, x; x:=-1; for n from 1 to q do a:=n;

t:=0; while ilog10(a)>0 do t:=t+1; b:=convert(a, base, 10);

a:=add(10^(k-1)*b[2*k-1], k=1..ceil(nops(b)/2))*add(10^(k-1)*b[2*k], k=1..trunc(nops(b)/2)); od; if t>x then x:=t; print(n);

fi; od; end: P(10^9); # Paolo P. Lava, Aug 01 2018

MATHEMATICA

f[n_] := Block[{d = IntegerDigits@ n}, If[OddQ@ Length@ d, PrependTo[d, 0]]; Times @@ FromDigits /@ Transpose@ Partition[d, 2]]; a[n_] := Block[ {c=-1, m}, t=0; While[c != n, t++; m=t; c=0; While[m > 9, c++; m = f@ m]]; t]; a /@ Range[0, 12] (* Giovanni Resta, Aug 01 2018 *)

CROSSREFS

Cf. A087471, A087472, A087474.

Sequence in context: A154057 A074814 A002600 * A014120 A003001 A198377

Adjacent sequences:  A087470 A087471 A087472 * A087474 A087475 A087476

KEYWORD

nonn,base

AUTHOR

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

EXTENSIONS

More terms from Ray Chandler, Sep 19 2003

a(30)-a(33) from Giovanni Resta, Aug 01 2018

STATUS

approved

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Last modified November 30 01:58 EST 2020. Contains 338780 sequences. (Running on oeis4.)