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Search: id:A003226
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| A003226 |
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Automorphic numbers: n^2 ends with n. Also m-morphic numbers for all m not equal to 6 (mod 10).
(Formerly M3752)
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+0
15
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| 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625, 87109376, 212890625, 787109376, 1787109376, 8212890625, 18212890625, 81787109376, 918212890625, 9918212890625, 40081787109376, 59918212890625
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Also called curious numbers.
For entries after the second, two successive terms sum up to a total having the form 10^n + 1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 29 2005
Substring of both its square and its cube not congruent to 0 (mod 10). See A029943 - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 16 2005.
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REFERENCES
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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.
B. A. Naik, 'Automorphic numbers' in 'Science Today'(subsequently renamed '2001') May 1982 pp. 59, Times of India, Mumbai.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to automorphic numbers
W. Schneider, Automorphic Numbers
W. Schneider, Automorphic Numbers
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CROSSREFS
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Equals {0,1} union A007185 union A016090.
Cf. A035383, A052228, A033819.
Sequence in context: A136888 A038248 A046831 this_sequence A137081 A137079 A121180
Adjacent sequences: A003223 A003224 A003225 this_sequence A003227 A003228 A003229
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001
Edited by David W. Wilson, Sep 26, 2002
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