x vs Δk — Cycle Animation Gallery

Each animation shows one full cycle on the x vs Δk plot. Cycle element links open the interactive explorer at that element. Parameters: o = number of odd steps; e = total h-exponent; d = h^e−g^o; k̂ = ∑_j g^o−1−jh^j; f = gcd(k,d) (common factor of all k values; q·f = d); q = d/f; x = k/f.

OEEOOEEE — p=281, g=3, h=2

g=3 h=2 o=3 e=5 d=5 k̂=19 f=5 q=1 Δk_max=30

p	OE	parity	x	k	Δk
281	OEEOOEEE	odd	5	25	6
396	EEOOEEEO	even	16	80	61
326	EOOEEEOE	even	8	40	21
291	OOEEEOEE	odd	4	20	1
401	OEEEOEEO	odd	13	65	46
456	EEEOEEOO	even	40	200	181
356	EEOEEOOE	even	20	100	81
306	EOEEOOEE	even	10	50	31

OEOEEOEE — p=293, g=3, h=2

g=3 h=2 o=3 e=5 d=5 k̂=19 f=1 q=5 Δk_max=30

p	OE	parity	x	k	Δk
293	OEOEEOEE	odd	23	23	4
402	EOEEOEEO	even	74	74	55
329	OEEOEEOE	odd	37	37	18
420	EEOEEOEO	even	116	116	97
338	EOEEOEOE	even	58	58	39
297	OEEOEOEE	odd	29	29	10
404	EEOEOEEO	even	92	92	73
330	EOEOEEOE	even	46	46	27

OOOEEEOEEEE — p=2119, g=3, h=2

g=3 h=2 o=4 e=7 d=47 k̂=65 f=47 q=1 Δk_max=266

p	OE	parity	x	k	Δk
2119	OOOEEEOEEEE	odd	1	47	−18
3107	OOEEEOEEEEO	odd	4	188	123
3601	OEEEOEEEEOO	odd	13	611	546
3848	EEEOEEEEOOO	even	40	1880	1815
2948	EEOEEEEOOOE	even	20	940	875
2498	EOEEEEOOOEE	even	10	470	405
2273	OEEEEOOOEEE	odd	5	235	170
3184	EEEEOOOEEEO	even	16	752	687
2616	EEEOOOEEEOE	even	8	376	311
2332	EEOOOEEEOEE	even	4	188	123
2190	EOOOEEEOEEE	even	2	94	29

OEOOEOOEEEEEE — p=8301, g=3, h=2

g=3 h=2 o=5 e=8 d=13 k̂=211 f=13 q=1 Δk_max=910

p	OE	parity	x	k	Δk
8301	OEOOEOOEEEEEE	odd	13	169	−42
12342	EOOEOOEEEEEEO	even	40	520	309
10267	OOEOOEEEEEEOE	odd	20	260	49
13325	OEOOEEEEEEOEO	odd	61	793	582
14854	EOOEEEEEEOEOO	even	184	2392	2181
11523	OOEEEEEEOEOOE	odd	92	1196	985
13953	OEEEEEEOEOOEO	odd	277	3601	3390
15168	EEEEEEOEOOEOO	even	832	10816	10605
11680	EEEEEOEOOEOOE	even	416	5408	5197
9936	EEEEOEOOEOOEE	even	208	2704	2493
9064	EEEOEOOEOOEEE	even	104	1352	1141
8628	EEOEOOEOOEEEE	even	52	676	465
8410	EOEOOEOOEEEEE	even	26	338	127