A087471 - OEIS

%I #8 Dec 05 2014 17:52:55

%S 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,

%T 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,

%U 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

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

%C 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).

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

%H Harvey P. Dale, <a href="/A087471/b087471.txt">Table of n, a(n) for n = 1..1000</a>

%F 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.

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

%t 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 *)

%Y Cf. A087472, A087473, A087474.

%K nonn,base

%O 1,2

%A _Amarnath Murthy_ and _Paul D. Hanna_, Sep 11 2003