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).

15, 32, 96, 960, 5280, 640320

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