The Russell-Ocampo superset

We missed the Venerean midsummer 17 March - sorry, lads. To make up for it, on this the first day of spring here on Earth...

As sequel to McConaghy et al., Ryan Russell and Cesar Ocampo sketched out an algorithm for finding these and more. "And more" means:

the naming convention for the cycler orbits are of the form p-h-s-i, where the letters represent four numbers that uniquely identify a class of cyclers. For example, a cycler of the class 4-3-2-12 has a period of 4 synodic periods, includes 3 half-years allotted for full or half-rev returns, and includes 2 symmetric returns using the 12th solution, by ascending semi-major axis, from the multiple revolution Lambert problem.

Clearly the McConaghy-Longuski-Byrnes nPr formula is just pPr in the above, inversely n-0-1-i. Here they use i as the ith intersection of all the Lambert curves against the line of time-o'-flight, which time for Buzz was 15/7 start-planet (Earth) years. So for Mars: 1-0-1-6 is 1L1, the Aldrin. 1-0-1-5 would have been 1S1, -4 1L2, -2 1L3 and Lambert has no 1P4+. S is odd and L, even; i_MAX = 2r_MAX + 1. 1-0-1-7 is 1U0, for what that is worth.

For 4Pr, r taps out at 9. Again we count up: 4S8 for 4-0-1-1, and 4L1 will be 4-0-1-16. McConaghy suggested 4S6 (4-0-1-5) and 4S5 (4-0-1-7). Russell and Ocampo like any of that a good deal less than McConaghy did; instead, that duo offer 4-0-3-7. At the 6Pr level: 6-0-1-23, 6-0-1-25, 6-0-1-27, 6-0-1-29 are 6S9, 6S8, 6S7, 6S6 respectively. I extrapolate -1 would be 6S20 so, Lambert solutions start comin' hard-n'-fast up here. Another point is that when h>0, i isn't bounded by p even that much.

Venus-Earth dual-synod solutions count up from 2S76 as 2-0-1-1. My 2L4 is, then, 2-0-1-6.

OOPSIE 3/23: On further investigation, 2S7 has no solution; 2S6 was the 2-0-1-1.