A087471 - OEIS

A087471

Final digit resulting from iterations of the product of the two numbers formed from the alternating digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, 3, 6, 9, 2, 5, 8, 2, 8, 4, 0, 4, 8, 2, 6, 0, 8, 6, 6, 8, 0, 5, 0, 5, 0, 0, 0, 5, 0, 0, 0, 6, 2, 8, 8, 0, 8, 8, 6, 0, 0, 7, 4, 2, 6, 5, 8, 8, 0, 8, 0, 8, 6, 8, 6, 0, 6, 0, 8, 4, 0, 9, 8, 4, 8, 0, 0, 8, 4, 8, 0, 0, 0, 0, 0, 0

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OFFSET

1,2

COMMENTS

A087472(n) gives the number of iterations required for Murthy's function, f(n), to reach a single digit. 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).

Apart from the undefined a(0), the sequence differs from A031347 first at n=121. [From R. J. Mathar, Sep 11 2008]

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = a(f(n)), where f(n) is Murthy's function: f(1234)=13*24=312, f(12345)=135*24=3240, f(123456)=135*246=33210.

EXAMPLE

a(1234) = a(13*24) = a(312) = a(32*1) = a(32) = a(3*2) = 6.

MATHEMATICA

Table[NestWhile[With[{idn=IntegerDigits[#]}, FromDigits[Take[idn, {1, -1, 2}]] FromDigits[Take[idn, {2, -1, 2}]]]&, n, #>9&], {n, 110}] (* Harvey P. Dale, Dec 05 2014 *)

CROSSREFS

Cf. A087472, A087473, A087474.

Sequence in context: A062078 A371281 A031347 * A128212 A187844 A007954

Adjacent sequences: A087468 A087469 A087470 * A087472 A087473 A087474

KEYWORD

nonn,base

AUTHOR

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

STATUS

approved