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Search: id:A007395
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| A007395 |
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The all 2's sequence.
(Formerly M0208)
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+0
48
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| 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also the iterated factorials of the number 2: 2!, (2!)!, ((2!)!)! - Peter C. Heinig (algorithms(AT)gmx.de), Apr 16 2006
Continued fraction for 1+sqrt(2) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2006
From wavelength of the series limit in spectrum of hydrogen (Lyman, Balmer, Paschen, Brackett, Pfund, Humphreys, Hanson-Strong and conjectured eighth: third differences of A145646=912, 3646, 8204, 14584, 22788, 32814, are a(n) signed. See also first differences of A145646=A145647. For first member (1215.67, 6562.8, 18751, 40512, 74578, 123690?, 190570), values must be perfected. Then third differences 2732, 2732 will be regular for simple fourth differences. [From Paul Curtz (bpcrtz(AT)free.fr), Oct 15 2008]
Except for the first term of [A002378], if X=[A144396], Y=[A007395], A= [A002378], we have, for all other terms, Pell's equation: [A144396]^2 - [A002378]*[A007395]^2=1; (X^2-A*Y^2=1); example: 3^2-2*2^2=1; 5^2-6*2^2=1; 19^2-90*2^2=1, and so on. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 11 2009]
For n >= 0, let M(n) be the matrix with 1st row = (n n+1) and 2nd row = (n+2 n+3). Then a(n) = absolute value of det(M(n)). [From Kailasam Viswanathan Iyer (kvi(AT)nitt.edu), Apr 11 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.
Ron Hardin, Binary arrays with both rows and cols sorted, symmetries
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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G.f.: 2/(1-x) & E.g.f.: 2*e^x [From Mohammad K. Azarian (azarian(AT)evansville.edu), Dec 22 2008]
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MATHEMATICA
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Table[2, {105}]
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CROSSREFS
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Cf. A000004, A000012, A010701.
Cf. A144396, A002378 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 11 2009]
Sequence in context: A046698 A036453 A040000 this_sequence A055642 A138902 A036452
Adjacent sequences: A007392 A007393 A007394 this_sequence A007396 A007397 A007398
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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