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A140527 Number of primes p with height h(p) = 1 and fundamental units epsilon(p) < 10^n. 0
6, 11, 16, 22, 26, 38, 44, 53, 61, 73, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

From table on p. 12 of Hashimoto. Abstract: Sarnak obtained the asymptotic formula of the sum of the class numbers of indefinite binary quadratic forms from the prime geodesic theorem for the modular group. In the present paper, we show several asymptotic formulas of partial sums of the class numbers by using the prime geodesic theorems for the congruence subgroups of the modular group.

LINKS

Table of n, a(n) for n=2..12.

Yasufumi Hashimoto, Asymptotic formulas for partial sums of class numbers of indefinite binary quadratic forms, arXiv:0807.0056

EXAMPLE

The enumerated primes p with height h(p) = 1 and fundamental units epsilon(p) < 10^2 are {5, 2, 13, 29, 53, 17}.

With epsilon(p) < 10^3 the primes are {37, 173, 293, 101, 197}.

With epsilon(p) < 10^4 the primes are {61, 677, 149, 41, 317}.

With epsilon(p) < 10^5 the primes are {773, 629, 157, 557, 109}.

With epsilon(p) < 10^6 the primes are {461, 797, 2477, 1013, 509}.

With epsilon(p) < 10^7 the primes are {89, 941, 181, 113, 1877, 653, 73, 1493, 3533, 389, 277, 1613}.

With epsilon(p) < 10^8 the primes are {397, 137, 2693, 1637, 1277, 1997}.

With epsilon(p) < 10^9 the primes are {373, 97, 821, 2309, 349, 701, 4157, 853, 1181}.

With epsilon(p) < 10^10 the primes are {4973, 233, 2357, 4373, 4253, 2957, 3797, 613}.

With epsilon(p) < 10^11 the primes are {1109, 3989, 353, 1949, 997, 1733, 1973, 4517, 2621, 7013, 9173}.

With epsilon(p) < 10^12 the primes are {1061, 2333, 4133, 1301, 2789, 421, 5309, 877, 3677, 3461, 10853, 2141}.

CROSSREFS

Sequence in context: A242594 A184487 A085813 * A191158 A208719 A208775

Adjacent sequences:  A140524 A140525 A140526 * A140528 A140529 A140530

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Jul 03 2008

STATUS

approved

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Last modified August 23 15:37 EDT 2014. Contains 246000 sequences.