A165736 a(n) = n^n^n^n^n^n^n^n^n^n^... read mod 10^10.

1, 1432948736, 2464195387, 411728896, 8408203125, 7447238656, 1565172343, 9695225856, 7392745289, 0, 9172666611, 6254012416, 4655045053, 7567502336, 5380859375, 290415616, 5320085777, 5354315776, 609963179, 0, 4460652421, 2551504896, 1075718247, 1076734976

Offset

1,2

Comments

Of course leading zeros are omitted.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Power Tower.

Formula

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.

Example

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.

Maple

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

Crossrefs

Sequence in context: A069320 A274902 A129249 * A372106 A048051 A345337

Adjacent sequences: A165733 A165734 A165735 * A165737 A165738 A165739

Keyword

nonn,base

Author

Ivan Panchenko, Sep 25 2009

Extensions

Edited (but not checked) by N. J. A. Sloane, Sep 28 2009

Corrected and extended by Alois P. Heinz, Sep 28 2009

Status

approved