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%I #28 Feb 27 2024 09:42:29
%S 0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,4,9,16,25,36,49,64,81,0,
%T 1,8,27,64,125,216,343,512,729,0,1,16,81,256,625,1296,2401,4096,6561,
%U 0,1,32,243,1024,3125,7776,16807,32768,59049,0,1,64,729,4096,15625,46656
%N Sequence of numbers after 1st step of iteration defined in A175419.
%H Stefano Spezia, <a href="/A175420/b175420.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = (((D_k^D_(k-1))^D_(k-2))^...)^D_1, where D_k = k-th digit D of number n and k = the number of digits of number n in decimal expansion of n (A055642).
%e For n = 33: a(33) = 27 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 1st step of the iteration ends with 27.
%p A175420 := proc(n) 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: seq(A175420(n),n=0..120) ; # _R. J. Mathar_, May 12 2010
%t Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; a[0]=0; a[n_]:=If[(len=IntegerLength[n])==1, n, Last[list=IntegerDigits[n]]^Product[Part[Drop[list, -1], i], {i, len-1}]]; Array[a, 67, 0] (* _Stefano Spezia_, Feb 25 2024 *)
%o (PARI) a(n) = if (n, my(d=digits(n), r=d[#d]); forstep (k=#d-1, 1, -1, r = r^d[k];); r); \\ _Michel Marcus_, Jan 20 2022
%Y Cf. A175419, A175421, A175422, A175423, A175424, A175425, A175426, A175427.
%Y Cf. A055642.
%K nonn,base,look
%O 0,3
%A _Jaroslav Krizek_, May 09 2010
%E More terms from _R. J. Mathar_, May 12 2010
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