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

Author

Jaroslav Krizek, May 09 2010

Keywords

• nonn
• base

Examples

			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
		

Crossrefs

Cf. A175419, A175420, A175421, A175422, 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) ; 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]

Extensions

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

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