A077466 -id:A077466 - cp's OEIS frontend

A077465 Values of n such that A006046(n)/n^theta, where theta=log(3)/log(2), is a local minimum, computed according to Harborth's recurrence.

1, 3, 5, 11, 21, 43, 87, 173, 347, 693, 1387, 2775, 5549, 11099, 22197, 44395, 88789, 177579, 355159, 710317, 1420635, 2841269, 5682539, 11365079, 22730157, 45460315, 90920629, 181841259, 363682519, 727365037, 1454730075

Offset: 1

Eric W. Weisstein, Nov 05 2002

nonn

Harborth's recurrence can miss local minima that are 2 less than values in this sequence. A complete listing of cumulative minima is given by A084230.

H. Harborth, Number of Odd Binomial Coefficients, Proc. Amer. Math. Soc. 62, 19-22, 1977.
Eric Weisstein's World of Mathematics, Stolarsky-Harborth Constant

Cf. A006046, A077464, A077466, A077467, A084230.

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).

Original entry on oeis.org

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

Eric W. Weisstein, Nov 06 2002

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

			0.812556559016006387694882...

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

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.

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

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

A077467 Sum of binary digits of A077465(n).

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41, 42, 43, 43, 44

Offset: 1

Eric W. Weisstein, Nov 05 2002

H. Harborth, Number of Odd Binomial Coefficients, Proc. Amer. Math. Soc. 62, 19-22, 1977.
Eric Weisstein's World of Mathematics, Stolarsky-Harborth Constant

Cf. A006046, A077464, A077465, A077466.

cp's OEIS Frontend

A077465 Values of n such that A006046(n)/n^theta, where theta=log(3)/log(2), is a local minimum, computed according to Harborth's recurrence.

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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).

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A077467 Sum of binary digits of A077465(n).

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