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

Offset: 1

Author

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

Keywords

• nonn
• base

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]

Examples

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

Links

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

Crossrefs

Cf. A087472, A087473, A087474.

Programs

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 *)

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.