A227097 a(n) = n successive applications of the <*>(3,2) operator to 1.

1, 3, 9, 27, 61, 123, 349, 1007, 2021, 4043, 8089, 16187, 42481, 125363, 271029, 612067, 1234141, 3498383, 10087069, 20254147, 40558401, 81167203, 163394609, 429879827, 1268830461, 2745691323, 6196472949, 12499016807, 35407044421, 101221129243, 202643278689

Offset

0,2

Comments

x<*>(3,2) means that the number obtained from digits of x are alternatively multiplicated by 3 and by 2 from right to left (taking carries into account).

a(n) = (...(1<*>(3,2))<*>(3,2))...<*>(3,2) (n recursive applications of the <*>(3,2) operator.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

V. Shevelev, Partition of multiplication

Example

a(0) = 1 (no operation)
a(2) = 1*3
a(3) = (1*3)*3 = 9
a(4) = ((1*3)*3)*3 = 27
a(5) = (27)<*>(3,2) = [2*2,7*3] = 40 + 21 = 61
a(6) = (61)<*>(3,2) = [2*6,1*3] = 120+3 = 123

Maple

a:= proc(n) option remember; local i, m, r;
      if n=0 then 1
    else m, r:= a(n-1), 0;
         for i from 0 while m>0 do
           r:= r +10^i *irem(m, 10, 'm') *(3-irem(i, 2))
         od; r
      fi
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 05 2013

Mathematica

ShDM[n_, {a_, b_}] :=
Module[{ex = 0},
  Plus @@
   FoldList[(10^ex)*#2*{a, b}[[1 + Mod[ex++, 2]]] &, 0,
    Reverse@IntegerDigits[n, 10]]];
NestList[ShDM[#, {3, 2}] &, 1, 25]

Crossrefs

Sequence in context: A015955 A357008 A097803 * A201202 A260938 A274626

Adjacent sequences: A227094 A227095 A227096 * A227098 A227099 A227100

Keyword

nonn,base

Author

Vladimir Shevelev, Jul 01 2013

Extensions

Example, Mathematica program, extension and corrected definition by Olivier Gérard, Jul 05 2013

Status

approved