Module:Sequence

Module documentation[view] [edit] [history] [purge]

This module primarily serves as a library for other modules and has no corresponding template.

Introspection summary for Module:Sequence
Functions provided (1) Line Function Params 3 contains (seq, n)	Lua modules required (0) Variable Module Functions used

No function descriptions were provided. The Lua code may have further information.

---

local p = {}

function p.contains(seq, n)
	if n > seq[#seq] then
		return nil
	end
	for i = 1, #seq do
		if seq[i] == n then
			return true
		end
	end
	return false
end

-- OEIS A117536
p.zeta_peak = {
	0, 1, 2, 3, 4,
	5, 7, 10, 12, 19,
	22, 27, 31, 41, 53,
	72, 99, 118, 130, 152,
	171, 217, 224, 270, 342,
	422, 441, 494, 742, 764,
	935, 954, 1012, 1106, 1178,
	1236, 1395, 1448, 1578, 2460,
	2684, 3395, 5585, 6079, 7033,
	8269, 8539, 11664, 14348, 16808,
	28742, 34691,
	-- unconfirmed data from [[The Riemann zeta function and tuning #Zeta EDO lists]]
	36269, 57578, 58973, 95524, 102557,
	112985, 148418, 212147, 241200
}

-- OEIS A117538
p.zeta_integral = {
	2, 5, 7, 12, 19,
	31, 41, 53, 72, 130,
	171, 224, 270, 764, 954,
	1178, 1395, 1578, 2684, 3395,
	7033, 8269, 8539, 14348, 16808,
	36269, 58973
}

-- OEIS A117537
p.zeta_gap = {
	2, 3, 5, 7, 12,
	19, 31, 46, 53, 72,
	270, 311, 954, 1178, 1308,
	1395, 1578, 3395, 4190,
	-- unconfirmed data from [[The Riemann zeta function and tuning #Zeta EDO lists]]
	8539, 14348, 58973, 95524
}

-- square superparticular indices by prime limit
-- counted by OEIS A117582
-- see https://github.com/lucasaugustus/oeis/blob/main/stormer.py
p.square_superpartuculars = {
	[2] = {},
	[3] = {2, 3},
	[5] = {4, 5, 9},
	[7] = {6, 7, 8, 15, 49},
	[11] = {10, 11, 21, 55, 99},
	[13] = {12, 13, 14, 25, 26, 27, 64, 65, 351},
	[17] = {16, 17, 33, 34, 35, 50, 51, 120, 169, 441},
	[19] = {18, 19, 20, 39, 56, 76, 77, 153, 170, 209, 324, 2431},
	[23] = {22, 23, 24, 45, 69, 91, 161, 208, 323, 391, 2024},
	[29] = {28, 29, 57, 115, 116, 144, 175, 231, 289, 494, 551, 783, 1275, 2001, 3249, 9801, 13311},
	[31] = {30, 31, 32, 63, 92, 125, 154, 155, 341, 342, 495, 528, 714, 1519, 1520, 13455},
	[37] = {36, 37, 38, 75, 111, 185, 186, 221, 260, 406, 407, 666, 703, 961, 1000, 1331, 1444, 1665, 1701, 2737, 3626, 5291, 7105, 17576},
	[41] = {40, 41, 81, 124, 204, 246, 247, 286, 287, 288, 369, 493, 575, 1024, 1025, 1189, 1518, 1681, 1682, 1886, 2295, 3773, 4960, 5083, 29601, 32799, 212381},
	[43] = {42, 43, 44, 85, 86, 87, 129, 171, 216, 259, 300, 343, 344, 559, 560, 645, 989, 1332, 1333, 1376, 1805, 1849, 2107, 2108, 2665, 2925, 4256, 4901, 5290, 10879, 10880, 11439, 134849},
}

return p