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%I #17 Feb 25 2024 10:21:33
%S 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,
%T 6561,1,25,216,1,8,1,0,1,6,1,1,1,1,1,1,1,0,1,8,1,1,
%U 867361737988403547205962240695953369140625,1,1,1,1,0,1,1,1,1,1,1,1,1,1
%N Sequence of numbers after 3rd step of iteration defined in A175419.
%e 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.
%p 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:
%p A175421 := proc(n) A175420(A175420(n)) ; end proc:
%p A175422 := proc(n) A175420(A175421(n)) ; end proc:
%p for n from 0 do printf("%d,\n",A175422(n)) ; end do; # _R. J. Mathar_, May 12 2010
%t 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 *)
%Y Cf. A175419, A175420, A175421, A175423, A175424, A175425, A175426, A175427.
%K nonn,base
%O 0,3
%A _Jaroslav Krizek_, May 09 2010
%E 7 more terms from _R. J. Mathar_, May 12 2010
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