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

0,3

Links

Stefano Spezia, Table of n, a(n) for n = 0..10000

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).

Example

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A175419, A175421, A175422, A175423, A175424, A175425, A175426, A175427.

Cf. A055642.

Sequence in context: A175422 A175423 A175421 * A062078 A371281 A031347

Adjacent sequences: A175417 A175418 A175419 * A175421 A175422 A175423

Keyword

nonn,base,look

Author

Jaroslav Krizek, May 09 2010

Extensions

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

Status

approved