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Powering the decimal digits of n (right-associative) with 0^0 = 1 by convention.
5

%I #57 Apr 10 2021 22:26:07

%S 1,2,3,4,5,6,7,8,9,1,1,1,1,1,1,1,1,1,1,1,2,4,8,16,32,64,128,256,512,1,

%T 3,9,27,81,243,729,2187,6561,19683,1,4,16,64,256,1024,4096,16384,

%U 65536,262144,1,5,25,125,625,3125,15625,78125,390625,1953125,1,6,36,216,1296

%N Powering the decimal digits of n (right-associative) with 0^0 = 1 by convention.

%C See A075877 for the left-associative version (which grows much more slowly). Usually the "^" operator is considered right-associative (so this is the "natural" version), i.e., a^b^c = a^(b^c) since (a^b)^c could be written a^(b*c) instead, while there is no such simplification for a^(b^c).

%C If n's first digit is succeeded by an odd number of consecutive 0's, a(n) is 1. If it is by an even number, a(n) is the first digit of n (A000030). - _Alex Costea_, Mar 27 2019

%H Alois P. Heinz, <a href="/A256229/b256229.txt">Table of n, a(n) for n = 1..237</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero">Zero to the power of zero</a>

%F a(n) = A075877(n) for n < 212.

%F a(n) = A133500(n) for n < 100.

%F a(10n+1) = a(n).

%e a(253) = 2^5^3 = 2^(5^3) = 2^125 = 42535295865117307932921825928971026432.

%p a:= proc(n) local m, r; m, r:= n, 1;

%p while m>0 do r:= irem(m, 10, 'm')^r od; r

%p end:

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Mar 19 2015

%t Power @@ IntegerDigits@ # & /@ Range@ 64 /. Indeterminate -> 1 (* _Michael De Vlieger_, Mar 21 2015 *)

%o (PARI) A256229(n,p=1)={until(!n\=10,p=(n%10)^p);p}

%o (Python)

%o def A256229(n):

%o ....y = 1

%o ....for d in reversed(str(n)):

%o ........y = int(d)**y

%o ....return y # _Chai Wah Wu_, Mar 21 2015

%Y Cf. A007953, A007954, A075877, A133500, A185969, A248907, A256179.

%K nonn,base,hear,look

%O 1,2

%A _M. F. Hasler_, Mar 19 2015

%E Incorrect comments deleted by _Alex Costea_, Mar 24 2019