A175423 Sequence of numbers after 4th 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, 216, 1, 1, 1, 0, 1, 8, 1, 1, 25, 36, 1, 8, 1, 0, 1, 6, 1, 1, 1, 1, 1, 1, 1, 0, 1, 8, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,3

Links

Table of n, a(n) for n=0..100.

Example

For n = 33: a(33) = 1 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 4th step of iteration ends with 1. - Jaroslav Krizek, May 09 2010

Maple

A175420 := proc(n) option remember; local dgs, a, i ; if n = 0 then return 0 ; end if; dgs := convert(n, base, 10) ; if op(1, dgs)= 0 then return 0 ; end if; for i from 1 to nops(dgs) do if op(-i, dgs) = 0 then dgs := [op(-i..nops(dgs), dgs)] ; dgs := subsop(1=1, dgs) ; break ; end if; end do: a := op(1, dgs) ; for i from 2 to nops(dgs) do a := a^ dgs[i] ; end do: a ; end proc:
A175421 := proc(n) A175420(A175420(n)) ; end proc:
A175422 := proc(n) A175420(A175421(n)) ; end proc:
A175423 := proc(n) A175420(A175422(n)) ; end proc:
seq(A175423(n), n=0..100) ; # 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, 4]; Array[a, 101, 0]

Crossrefs

Cf. A175419, A175420, A175421, A175422, A175424, A175425, A175426, A175427.

Sequence in context: A217657 A175419 A175422 * A175421 A175420 A062078

Adjacent sequences: A175420 A175421 A175422 * A175424 A175425 A175426

Keyword

nonn,base

Author

Jaroslav Krizek, May 09 2010

Extensions

More terms from R. J. Mathar, May 12 2010

a(100) corrected by Stefano Spezia, Feb 25 2024

Status

approved