A175420 Sequence of numbers after 1st 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, 16, 25, 36, 49, 64, 81, 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 0, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 0, 1, 64, 729, 4096, 15625, 46656
Offset: 0
Examples
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.
Links
- Stefano Spezia, Table of n, a(n) for n = 0..10000
Programs
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Maple
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
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Mathematica
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 *) -
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
Formula
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).
Extensions
More terms from R. J. Mathar, May 12 2010