A077464 Stolarsky-Harborth constant; lim inf_{n->oo} F(n)/n^theta, where F(n) is the number of odd binomial coefficients in the first n rows and theta=log(3)/log(2).

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

Offset

0,1

Comments

The limit supremum of F(n)/n^theta is 1. - Charles R Greathouse IV, Oct 30 2016

Named by Finch (2003) after Kenneth B. Stolarsky and Heiko Harborth. Stolarsky (1977) evaluated that its value is in the interval [0.72, 0.815], and Harborth (1977) calculated the value 0.812556. - Amiram Eldar, Dec 03 2020

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 145-151.

Links

Table of n, a(n) for n=0..100.

Heiko Harborth, Number of Odd Binomial Coefficients, Proc. Amer. Math. Soc., Vol. 62, No. 1 (1977), pp. 19-22.

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Periodic minimum in the count of binomial coefficients not divisible by a prime, arXiv:2408.06817 [math.NT], 2024. See pp. 2, 4.

Kenneth B. Stolarsky, Digital sums and binomial coefficients, Notices of the American Mathematical Society, Vol. 22, No. 6 (1975), A-669, entire volume.

Kenneth B. Stolarsky, Power and Exponential Sums of Digital Sums Related to Binomial Coefficient Parity, SIAM J. Appl. Math., Vol. 32, No. 4 (1977), pp. 717-730.

Eric Weisstein's World of Mathematics, Stolarsky-Harborth Constant.

Eric Weisstein's World of Mathematics, Pascal's Triangle.

Formula

Equals lim inf_{n->oo} A006046(n)/n^A020857. - Amiram Eldar, Dec 03 2020

Example

0.812556559016006387694882...

Crossrefs

Cf. A006046, A020857, A077465, A077466, A077467.

Sequence in context: A368146 A372426 A356022 * A088373 A375212 A154167

Adjacent sequences: A077461 A077462 A077463 * A077465 A077466 A077467

Keyword

nonn,cons

Author

Eric W. Weisstein, Nov 06 2002

Status

approved