A115632 Decimal expansion of asymptotic constant in Goebel's sequence A003504.

1, 0, 4, 7, 8, 3, 1, 4, 4, 7, 5, 7, 6, 4, 1, 1, 2, 2, 9, 5, 5, 9, 9, 0, 9, 4, 6, 2, 7, 4, 3, 1, 3, 7, 5, 5, 4, 5, 9, 0, 5, 8, 7, 6, 1, 2, 8, 6, 0, 2, 3, 3, 0, 9, 6, 9, 5, 1, 0, 4, 0, 6, 4, 8, 5, 3, 5, 3, 6, 0, 5, 9, 0, 4, 9, 7, 2, 6, 2, 3, 1, 7, 9, 7, 5, 1, 3, 0, 9, 7, 9, 0, 0, 0, 7, 0, 9, 9, 4, 7, 9, 5, 1, 1, 3

Offset

1,3

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.10, p. 446.

Links

Table of n, a(n) for n=1..105.

Hibiki Gima, Toshiki Matsusaka, Taichi Miyazaki, and Shunta Yara, On integrality and asymptotic behavior of the (k,l)-Göbel sequences, arXiv:2402.09064 [math.NT], 2024. See p. 2.

Eric Weisstein's World of Mathematics, Goebel's Sequence.

Example

1.04783144757641122955990946274313755459058761286023309695104064853536...

Prog

(PARI) {a(n)=local(t=log(2)/2); for(k=2, 14, t+= (log(1+(k-1)/exp(2^(k-1)*t))-log(k))/2^k); t=exp(t-suminf(k=15, log(k)/2^k)); floor(t*10^(n-1))%10} /* Michael Somos, Apr 02 2006 */

Crossrefs

Cf. A003504.

Sequence in context: A198822 A275977 A151968 * A190260 A318383 A151958

Adjacent sequences: A115629 A115630 A115631 * A115633 A115634 A115635

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 27 2006

Status

approved