A165736 - OEIS

%I #21 Feb 13 2024 05:07:54

%S 1,1432948736,2464195387,411728896,8408203125,7447238656,1565172343,

%T 9695225856,7392745289,0,9172666611,6254012416,4655045053,7567502336,

%U 5380859375,290415616,5320085777,5354315776,609963179,0,4460652421,2551504896,1075718247,1076734976

%N a(n) = n^n^n^n^n^n^n^n^n^n^... read mod 10^10.

%C Of course leading zeros are omitted.

%C a(3) gives the last 10 digits of Graham's number.

%H Alois P. Heinz, <a href="/A165736/b165736.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>.

%F a(n) = n^(n^(n^(n^(n^(n^(n^(n^(n^(n^n mod 10) mod 100) mod 1000) mod 10000) mod 100000) mod 1000000) mod 10000000) mod 100000000) mod 1000000000) mod 10000000000.

%e 3^3 mod 10 = 7; 3^7 mod 100 = 87; 3^87 mod 1000 = 387; 3^387 mod 10000 = 5387; 3^5387 mod 100000 = 95387; 3^95387 mod 1000000 = 195387; 3^195387 mod 10000000 = 4195387; 3^4195387 mod 100000000 = 64195387; 3^64195387 mod 1000000000 = 464195387; 3^464195387 mod 10000000000 = 2464195387; so the last 10 digits of 3^3^3^3^3^3^3^3^3^3^3^3^3^... are 2464195387 and a(3) = 2464195387.

%p a:= proc(n) local i, m; if irem(n, 10)=0 then 0 else m:= n; for i from 1 to 10 do m:= n&^m mod 10^i od; m fi end: seq(a(n), n=1..30); # _Alois P. Heinz_, Sep 28 2009

%K nonn,base

%O 1,2

%A _Ivan Panchenko_, Sep 25 2009

%E Edited (but not checked) by _N. J. A. Sloane_, Sep 28 2009

%E Corrected and extended by _Alois P. Heinz_, Sep 28 2009