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
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)).
A267195 is a supersequence (negated).
A302142
a(n) = (-1) * round(j((1 + sqrt(-n))/2)), where j is j-invariant.
Original entry on oeis.org
-1728, -233, 0, 90, 539, 1539, 3375, 6511, 11663, 19897, 32768, 52512, 82306, 126616, 191658, 286008, 421407, 613808, 884736, 1263051, 1787217, 2508208, 3493226, 4830420, 6634880, 9056199, 12288000, 16579887, 22252407, 29715715, 39492794, 52248279, 68824132
Offset: 1
n | j((1 + sqrt(-n))/2) | a(n) | A056580(n) - 744
---+---------------------+---------+------------------
1 | -1728 | -1728 | -721
2 | -232.86... | -233 | -659
3 | 0 | 0 | -513
4 | 89.59... | 90 | -209
5 | 538.90... | 539 | 380
6 | 1539.19... | 1539 | 1454
7 | 3375 | 3375 | 3328
8 | 6511.17... | 6511 | 6484
9 | 11663.39... | 11663 | 11648
10 | 19897.28... | 19897 | 19888
11 | 32768 | 32768 | 32762
12 | 52511.98... | 52512 | 52508
13 | 82306.31... | 82306 | 82304
14 | 126616.31... | 126616 | 126615
15 | 191657.83... | 191658 | 191657
16 | 286007.99... | 286008 | 286007
17 | 421407.46... | 421407 | 421407
18 | 613808.31... | 613808 | 613808
19 | 884736 | 884736 | 884736
20 | 1263050.90... | 1263051 | 1263051
21 | 1787216.60... | 1787217 | 1787216
22 | 2508208.07... | 2508208 | 2508208
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