1,1

a(n)^2 == a(n) (mod 10^n), that is, a(n) is idempotent of Z[10^n].

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179.

R. A. Fairbairn, More on automorphic numbers, J. Rec. Math., 2 (No. 3, 1969), 170-174.

Jan Gullberg, Mathematics, From the Birth of Numbers, W. W. Norton & Co., NY, page 253-4.

Ya. I. Perelman, Algebra can be fun, pp. 97-98.

C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.

Xiaolong Ron Yu, Curious Numbers, Pi Mu Epsilon Journal, Spring 1999, pp. 819-823.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to automorphic numbers

a(n) = 5^(2^n) mod 10^n.

a(5) = 90625 because 90625^2 == 8212890625 ends in 90625.

A018247 gives associated 10-adic number.

A003226 = {0, 1} union (this sequence) union A016090.

Sequence in context: A082026 A101392 A078260 this_sequence A030995 A067270 A137114

Adjacent sequences: A007182 A007183 A007184 this_sequence A007186 A007187 A007188

nonn,base

N. J. A. Sloane (njas(AT)research.att.com).

More terms from David W. Wilson (davidwwilson(AT)comcast.net)

Edited by David W. Wilson, Sep 26, 2002