Module:Sequence

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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
	},
	[47] = {
		46, 47, 48, 93, 94, 95,
		187, 188, 189, 329, 375, 376, 377, 517, 704, 799, 846, 987, 988,
		1035, 1364, 1457, 1599, 2209, 2255, 2584, 4465, 6579, 7568,
		16169, 17577, 19551, 21385,
		192511
	},
	[53] = {
		52, 53, 54,
		105, 160, 265, 319, 370, 371, 424, 476, 529, 637, 689, 741, 847, 900, 901, 902,
		1377, 2015, 2755, 2915, 5831, 11661, 1749, 4929, 6149,
		23001, 23374, 27455, 36518, 62699,
		247456, 248676,
		1205645
	},
	[59] = {
		58, 59,
		117, 118, 119, 176, 235, 295, 296, 530, 531, 532, 589, 649, 650, 944, 945,
		1121, 1887, 2184, 2300, 2419, 3009, 3363, 5075, 5781, 6137, 6727, 6784, 6785, 7315, 8555,
		10620, 13689, 17051, 19942, 27435, 31212, 37583, 46138, 55224, 63426,
		956449
	},
}

return p