A199743 - OEIS

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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).

3

15, 32, 96, 960, 5280, 640320

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..6.

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

EXAMPLE

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

Cf. A003173, A305500.

A267195 is a supersequence (negated).

Sequence in context: A055809 A112147 A007256 * A331551 A180815 A336625

Adjacent sequences: A199740 A199741 A199742 * A199744 A199745 A199746

KEYWORD

nonn,fini,full

AUTHOR

Artur Jasinski, Nov 09 2011

STATUS

approved