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A256229 Powering the decimal digits of n (right-associative) with 0^0 = 1 by convention.

%I A256229 #59 May 22 2025 10:21:42
%S A256229 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 A256229 3,9,27,81,243,729,2187,6561,19683,1,4,16,64,256,1024,4096,16384,
%U A256229 65536,262144,1,5,25,125,625,3125,15625,78125,390625,1953125,1,6,36,216,1296
%N A256229 Powering the decimal digits of n (right-associative) with 0^0 = 1 by convention.
%C A256229 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 A256229 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 A256229 Alois P. Heinz, <a href="/A256229/b256229.txt">Table of n, a(n) for n = 1..237</a>
%H A256229 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero">Zero to the power of zero</a>
%F A256229 a(n) = A075877(n) for n < 212.
%F A256229 a(n) = A133500(n) for n < 100.
%F A256229 a(10n+1) = a(n).
%e A256229 a(253) = 2^5^3 = 2^(5^3) = 2^125 = 42535295865117307932921825928971026432.
%p A256229 a:= proc(n) local m, r; m, r:= n, 1;
%p A256229       while m>0 do r:= irem(m, 10, 'm')^r od; r
%p A256229     end:
%p A256229 seq(a(n), n=1..100);  # _Alois P. Heinz_, Mar 19 2015
%t A256229 Power @@ IntegerDigits@ # & /@ Range@ 64 /. Indeterminate -> 1 (* _Michael De Vlieger_, Mar 21 2015 *)
%o A256229 (PARI) A256229(n,p=1)={until(!n\=10,p=(n%10)^p);p}
%o A256229 (Python)
%o A256229 def A256229(n):
%o A256229     y = 1
%o A256229     for d in reversed(str(n)):
%o A256229         y = int(d)**y
%o A256229     return y # _Chai Wah Wu_, Mar 21 2015
%Y A256229 Cf. A007953, A007954, A075877, A133500, A185969, A248907, A256179.
%K A256229 nonn,base,hear,look
%O A256229 1,2
%A A256229 _M. F. Hasler_, Mar 19 2015
%E A256229 Incorrect comments deleted by _Alex Costea_, Mar 24 2019