A085579 See comments lines for definition.

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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..100.

Formula

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..

Prog

(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])", "); ) }

Crossrefs

Sequence in context: A333182 A154489 A187832 * A081813 A197003 A048799

Adjacent sequences: A085576 A085577 A085578 * A085580 A085581 A085582

Keyword

easy,base,nonn

Author

Cino Hilliard, Jul 06 2003

Extensions

Edited by R. J. Mathar, Feb 01 2008

Status

approved