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Search: id:A085579
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| A085579 |
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See comments lines for definition. |
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+0
1
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| 9, 3, 1, 4, 8, 4, 2, 8, 6, 7, 0, 8, 0, 4, 4, 3, 8, 1, 7, 6, 8, 6, 4, 9, 9, 5, 3, 6, 3, 6, 1, 3, 7, 9, 3, 4, 1, 7, 1, 0, 8, 0, 2, 2, 1, 8, 2, 8, 3, 7, 2, 3, 1, 0, 2, 4, 4, 4, 6, 6, 6, 7, 2, 5, 9, 0, 2, 3, 2, 5, 2, 2, 7, 1, 6, 8, 7, 3, 3, 0, 8, 8, 0, 8, 1, 9, 1, 6, 5, 4, 2, 8, 3, 5, 4, 3, 9, 8, 0, 5
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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K = 2 in the script below. Conjecture: this diagonal expressed as a decimal is irrational and transcendental. Proof? Counterexample?
Write down the floating point constants x(m)>0 which solve x^2+mx=2, one per row for m=1,2,3,...:
0.99999999999999999999...
0.73205080756887729353...
0.56155281280883027491...
0.44948974278317809820...
0.37228132326901432993...
0.31662479035539984911...
and read this diagonally, the first digit after the dot from the first constant, the 2nd digit after the dot from the 2nd constant, the 3rd digit after the dot from the 3rd constant etc.
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FORMULA
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Also the decimal expansion of the positive solutions x of the quadratic equation x^2 + mx - 2 = 0, m = 1, 2... x = (sqrt(m^2+8)-2)/2 m=1, 2..
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PROGRAM
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(PARI) diagonal(n, k) = { default(realprecision, n); for(m=1, n, s=.1; for(x=1, n, s=k/(s+m); ); a = Vec(Str(s)); print1(eval(a[m+2])", "); ) }
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CROSSREFS
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Sequence in context: A093312 A154629 A154489 this_sequence A081813 A048799 A086232
Adjacent sequences: A085576 A085577 A085578 this_sequence A085580 A085581 A085582
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KEYWORD
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easy,base,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Jul 06 2003
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 01 2008
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