cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A032354 j-invariants for orders of class number 1.

Original entry on oeis.org

0, 1728, -3375, 8000, -32768, 54000, 287496, -884736, -12288000, 16581375, -884736000, -147197952000, -262537412640768000
Offset: 0

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Keywords

Comments

This sequence may also be written as [0, 12^3, -15^3, 20^3, -32^3, 2*30^3, 66^3, -96^3, -3*160^3, 255^3, -960^3, -5280^3, -640320^3]. Compare A267195. - N. J. A. Sloane, Jan 27 2016

References

  • H. Cohn, Introduction to the Construction of Class Fields, Cambridge; p. 183.
  • D. A. Cox, Primes of the form x^2+ny^2, Wiley, p. 261.

Crossrefs

See A267195 for (essentially) the cube roots of these numbers.
See A133675 (times -1) for the corresponding discriminants.

A199743 Rounded near-integers (exp(Pi*sqrt(h)) - 744)^(1/3) where h is A003173(n+3) (Heegner numbers of the form 4p-1 where p is prime).

Original entry on oeis.org

15, 32, 96, 960, 5280, 640320
Offset: 1

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Author

Artur Jasinski, Nov 09 2011

Keywords

Examples

			a(1) =     15 because     15^3 + 744 ~ exp(Pi*sqrt(7)).
a(2) =     32 because     32^3 + 744 ~ exp(Pi*sqrt(11)).
a(3) =     96 because     96^3 + 744 ~ exp(Pi*sqrt(19)).
a(4) =    960 because    960^3 + 744 ~ exp(Pi*sqrt(43)).
a(5) =   5280 because   5280^3 + 744 ~ exp(Pi*sqrt(67)).
a(6) = 640320 because 640320^3 + 744 ~ exp(Pi*sqrt(163)).
		

Crossrefs

A267195 is a supersequence (negated).

Formula

a(n) = (-j((1 + i*sqrt(h(n))) / 2))^(1/3) where h(n) = A003173(n+3) and j(x) is the j-invariant. - Andrey Zabolotskiy, Sep 30 2021

A357211 a(n) is the real cube root of the value of the j-function for the n-th Heegner number A003173(n).

Original entry on oeis.org

12, 20, 0, -15, -32, -96, -960, -5280, -640320
Offset: 1

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Crossrefs

Showing 1-3 of 3 results.