A087471 -id:A087471 - cp's OEIS frontend

A080464 Product of the two numbers formed by alternate digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0

Offset: 10

Amarnath Murthy, Mar 02 2003

			a(132546) = 124 * 356 = 44144.

M. F. Hasler, Table of n, a(n) for n = 10..10000

Cf. A007954, A080463, A080465, A087471, A087472, A087473, A087474.

nad[n_]:=Module[{idn=IntegerDigits[n]},FromDigits[Take[idn,{1,-1,2}]] FromDigits[ Take[idn,{2,-1,2}]]]; Array[nad,120,10] (* Harvey P. Dale, Aug 07 2019 *)

A080464(n,d=digits(n))={n=d*matrix(#d,2,z,s,if((z-s)%2,10^((#d-z)\2)));n[1]*n[2]}

a(n) < n for all n. - M. F. Hasler, Jan 10 2016

More terms from Ray Chandler, Oct 11 2003

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.

Original entry on oeis.org

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

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

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]

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

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

Cf. A087471, A087473, A087474.

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

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.

Original entry on oeis.org

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

Offset: 0

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

			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.

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

Cf. A087471, A087472, A087474.

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 *)

More terms from Ray Chandler, Sep 19 2003

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

A087474 Triangle T(n,k), read by rows, in which the n-th row gives the n successive iterations of f(m) on A087473(n), where f(m) is product of the two numbers formed from the alternating digits of m.

Original entry on oeis.org

1, 10, 0, 25, 10, 0, 39, 27, 14, 4, 77, 49, 36, 18, 8, 171, 77, 49, 36, 18, 8, 199, 171, 77, 49, 36, 18, 8, 577, 399, 351, 155, 75, 35, 15, 5, 887, 696, 594, 486, 368, 228, 56, 30, 0, 1592, 988, 784, 592, 468, 288, 224, 48, 32, 6, 2682, 1736, 988, 784, 592, 468, 288, 224

Offset: 0

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

			The 4th row is {77,49,36,18,8} since f(77)=49, f(49)=36, f(36)=18, f(18)=8.
{1},
{10,0},
{25,10,0},
{39,27,14,4},
{77,49,36,18,8},
{171,77,49,36,18,8},
{199,171,77,49,36,18,8},
{577,399,351,155,75,35,15,5},...

Cf. A087471, A087472, A087473.

T(0, 0)=1, T(n, 0)=A087473(n), T(n, k+1) = f(T(n, k)), where f(m) is the product of the two numbers formed by the alternating digits of m.

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A080464 Product of the two numbers formed by alternate digits of n.

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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.

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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.

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A087474 Triangle T(n,k), read by rows, in which the n-th row gives the n successive iterations of f(m) on A087473(n), where f(m) is product of the two numbers formed from the alternating digits of m.

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