cp's OEIS Frontend

A075877 Powering the decimal digits of n (left-associative).

%I A075877 #14 Mar 22 2015 09:19:36
%S A075877 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 A075877 3,9,27,81,243,729,2187,6561,19683,1,4,16,64,256,1024,4096,16384,
%U A075877 65536,262144,1,5,25,125,625,3125,15625,78125,390625,1953125,1,6,36,216,1296
%N A075877 Powering the decimal digits of n (left-associative).
%C A075877 See A256229 for the (maybe more natural) "right-associative" variant, a(xyz)=x^(y^z). a(n) = A256229(n) for n < 212 (up to 210, according to the 2nd formula which also holds for A256229), but (2^1)^2 = 4 while 2^(1^2) = 1. - _M. F. Hasler_, Mar 22 2015
%H A075877 Reinhard Zumkeller, <a href="/A075877/b075877.txt">Table of n, a(n) for n = 1..10000</a>
%F A075877 a(n) = if n < 10 then n else a(floor(n\10))^(n mod 10).
%F A075877 a(n) = 1 iff the initial digit is 1 or n contains a 0 (i.e., A055641(n) > 0 or A000030(n) = 1);
%F A075877 a(A011540(n)) = 1.
%F A075877 a(n) = A133500(n) for n <= 99. - _Reinhard Zumkeller_, May 27 2013
%e A075877 a(253) = (2^5)^3 = 32^3 = 32768.
%o A075877 (Haskell)
%o A075877 a075877 n = if n < 10 then n else a075877 (n `div` 10) ^ (n `mod` 10)
%o A075877 -- _Reinhard Zumkeller_, May 27 2013
%o A075877 (PARI) A075877(n)=if(n>9,A075877(n\10)^(n%10),n) \\ _M. F. Hasler_, Mar 19 2015
%Y A075877 Cf. A007953, A007954.
%Y A075877 Cf. A185969, A248907, A256179.
%K A075877 nonn,base,hear,look
%O A075877 1,2
%A A075877 _Reinhard Zumkeller_, Oct 16 2002
%E A075877 Formula corrected by _Reinhard Zumkeller_, May 27 2013
%E A075877 Edited by _M. F. Hasler_, Mar 22 2015