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A175423 Sequence of numbers after 4th step of iteration defined in A175419.

%I A175423 #17 Feb 25 2024 10:21:54
%S A175423 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,
%T A175423 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,
%U A175423 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
%N A175423 Sequence of numbers after 4th step of iteration defined in A175419.
%e A175423 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
%p A175423 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:
%p A175423 A175421 := proc(n) A175420(A175420(n)) ; end proc:
%p A175423 A175422 := proc(n) A175420(A175421(n)) ; end proc:
%p A175423 A175423 := proc(n) A175420(A175422(n)) ; end proc:
%p A175423 seq(A175423(n),n=0..100) ; # _R. J. Mathar_, May 12 2010
%t A175423 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]
%Y A175423 Cf. A175419, A175420, A175421, A175422, A175424, A175425, A175426, A175427.
%K A175423 nonn,base
%O A175423 0,3
%A A175423 _Jaroslav Krizek_, May 09 2010
%E A175423 More terms from _R. J. Mathar_, May 12 2010
%E A175423 a(100) corrected by _Stefano Spezia_, Feb 25 2024