A077464 - OEIS

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).

%I #30 Aug 16 2024 16:42:00

%S 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,

%T 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,

%U 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

%N 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).

%C The limit supremum of F(n)/n^theta is 1. - _Charles R Greathouse IV_, Oct 30 2016

%C 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

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

%H Heiko Harborth, <a href="http://dx.doi.org/10.1090/S0002-9939-1977-0429714-1">Number of Odd Binomial Coefficients</a>, Proc. Amer. Math. Soc., Vol. 62, No. 1 (1977), pp. 19-22.

%H Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2408.06817">Periodic minimum in the count of binomial coefficients not divisible by a prime</a>, arXiv:2408.06817 [math.NT], 2024. See pp. 2, 4.

%H Kenneth B. Stolarsky, Digital sums and binomial coefficients, Notices of the American Mathematical Society, Vol. 22, No. 6 (1975), A-669, <a href="https://www.ams.org/journals/notices/197510/197510FullIssue.pdf">entire volume</a>.

%H Kenneth B. Stolarsky, <a href="https://doi.org/10.1137/0132060">Power and Exponential Sums of Digital Sums Related to Binomial Coefficient Parity</a>, SIAM J. Appl. Math., Vol. 32, No. 4 (1977), pp. 717-730.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Stolarsky-HarborthConstant.html">Stolarsky-Harborth Constant</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PascalsTriangle.html">Pascal's Triangle</a>.

%F Equals lim inf_{n->oo} A006046(n)/n^A020857. - _Amiram Eldar_, Dec 03 2020

%e 0.812556559016006387694882...

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

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Nov 06 2002