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Search: id:A018248
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| A018248 |
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The 10-adic integer x = ...1787109376 satisfies x^2 = x. |
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+0
12
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| 6, 7, 3, 9, 0, 1, 7, 8, 7, 1, 8, 0, 0, 4, 7, 3, 4, 7, 7, 0, 6, 2, 2, 0, 0, 8, 3, 3, 9, 8, 5, 9, 9, 0, 9, 8, 3, 0, 1, 9, 6, 7, 6, 7, 5, 6, 7, 5, 2, 4, 4, 9, 9, 9, 8, 8, 1, 6, 3, 1, 9, 1, 4, 0, 9, 4, 3, 3, 8, 7, 3, 9, 9, 0, 1, 0, 9, 4, 1, 6, 0, 7, 9, 1, 0, 3, 8, 1, 9, 8, 0, 8, 6, 2, 9, 9, 6, 4, 0, 6, 9, 0, 6, 3, 7, 5, 3, 2
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The 10-adic numbers a and b defined in A018247 and this sequence satisfy a^2=a, b^2=b, a+b=1, ab=0.
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REFERENCES
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W. W. R. Ball, Mathematical Recreations & Essays, N.Y. Macmillan Co, 1947.
R. Cuculiere, Jeux Mathematiques, in Pour la Science, No. 6 (1986), 10-15.
M. Kraitchik, Sphinx, 1935, p. 1.
A. M. Robert, A Course in p-adic Analysis, Springer, 2000; see pp. 63, 419.
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LINKS
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Paul D. Hanna, Table of n, a(n) for n = 0..999
Anonymous, Automorphic numbers (2)
Eric Weisstein's World of Mathematics, Automorphic numbers (1)
Index entries for sequences related to automorphic numbers
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FORMULA
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x = r^4 where r=...1441224165530407839804103263499879186432 (A120817). x = 10-adic limit_{n->infty} 6^(5^n). - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 06 2006
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EXAMPLE
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x equals the limit of the (n+1) trailing digits of 6^(5^n):
6^(5^0)=(6), 6^(5^1)=77(76), 6^(5^2)=28430288029929701(376),...
x = ...9442576576769103890995893380022607743740081787109376.
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MATHEMATICA
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b = {6}; g[n_] := Block[{k = 0, c}, While[c = FromDigits[Prepend[b, k]]; Mod[c^2, 10^n] != c, k++ ]; b = Prepend[b, k]]; Do[ g[n], {n, 2, 105}]; Reverse[b]
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PROGRAM
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(PARI) {a(n)=local(b=6, v=[]); for(k=1, n+1, b=b^5%10^k; v=concat(v, (10*b\10^k))); v[n+1]} - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 06 2006
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CROSSREFS
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A016090 gives associated automorphic numbers.
Cf. A018247, A033819.
The difference between this sequence & A018247 is A075693 and their product is A075693.
Cf. A120817, A120818, A091664.
Sequence in context: A154339 A139350 A092560 this_sequence A146485 A049254 A144028
Adjacent sequences: A018245 A018246 A018247 this_sequence A018249 A018250 A018251
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KEYWORD
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base,nonn
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AUTHOR
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Yoshihide Tamori (yo(AT)salk.edu)
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net). Comments from Michael Somos.
Edited by David W. Wilson, Sep 26, 2002
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