A175422 Sequence of numbers after 3rd step of iteration defined in A175419.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 4, 9, 6, 25, 36, 1, 1, 1, 0, 1, 8, 6561, 1, 25, 216, 1, 8, 1, 0, 1, 6, 1, 1, 1, 1, 1, 1, 1, 0, 1, 8, 1, 1, 867361737988403547205962240695953369140625, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Jaroslav Krizek, May 09 2010

Keywords

• nonn
• base

Examples

			For n = 33: a(33) = 6561 because for the number 33 there are 4 steps of defined iteration: {3^3 = 27}, {7^2 = 49}, {9^4 = 6561}, {((1^6)^5)^6 = 1} and the 3rd step of the iteration ends with 6561.
		

Crossrefs

Cf. A175419, A175420, A175421, A175423, A175424, A175425, A175426, A175427.

Programs

Maple

A175420 := proc(n) option remember; local dgs,a,i ; if n = 0 then return 0 ; end if; dgs := convert(n,base,10) ; a := op(1,dgs) ; for i from 2 to nops(dgs) do a := a^ op(i,dgs) ; end do: a ; end proc:
A175421 := proc(n) A175420(A175420(n)) ; end proc:
A175422 := proc(n) A175420(A175421(n)) ; end proc:
for n from 0 do printf("%d,\n",A175422(n)) ; end do; # R. J. Mathar, May 12 2010

Mathematica

Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; A175420[0]=0; A175420[n_]:=If[(len=IntegerLength[n])==1, n, Last[list=IntegerDigits[n]]^Product[Part[Drop[list, -1], i], {i, len-1}]]; a[n_]:=Nest[A175420[#]&,n,3]; Array[a, 70, 0] (* Stefano Spezia, Feb 25 2024 *)

Extensions

7 more terms from R. J. Mathar, May 12 2010