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A016090 Automorphic numbers ending in digit 6. 11
6, 76, 376, 9376, 9376, 109376, 7109376, 87109376, 787109376, 1787109376, 81787109376, 81787109376, 81787109376, 40081787109376, 740081787109376, 3740081787109376, 43740081787109376, 743740081787109376 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

Also called congruent numbers.

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

REFERENCES

R. Cuculiere, Jeux Mathematiques, in Pour la Science, No. 6 (1986), 10-15.

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.

A. M. Robert, A Course in p-adic Analysis, Springer, 2000; see pp. 63, 419.

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.

LINKS

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

Index entries for sequences related to automorphic numbers

FORMULA

a(n) = 16^(5^n) mod 10^n.

EXAMPLE

a(5) = 09376 because 09376^2 == 87909376 ends in 09376.

CROSSREFS

A018248 gives associated 10-adic number.

A003226 = {0, 1} union A007185 union (this sequence).

Sequence in context: A126462 A081066 A185289 * A181343 A137132 A053337

Adjacent sequences:  A016087 A016088 A016089 * A016091 A016092 A016093

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v (rgwv(AT)rgwv.com), Dave Wilson (davidwwilson(AT)comcast.net)

EXTENSIONS

Edited by David W. Wilson, Sep 26, 2002

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Last modified February 13 02:03 EST 2012. Contains 205435 sequences.