
COMMENTS

It is remarkable that, if we note with p the numbers from sequence, for every p was obtained a prime, a squarefree semiprime or a number divisible by 5 through the formula 3*p + 4.
Primes obtained and the corresponding p in the brackets: 43(13), 61(19), 97(31), 73(23), 127(41), 223(73), 37(11), 113(103), 307(101), 331(109), 601(199), 1303(433), 19(5), 457(151), 421(139), 547(181), 2221(739), 691(229), 757(251), 3967(1321), 727(241), 163(53), 3517(1171), 1063(353), 1783(593), 1987(661), 1861(619), 271(89), 6271(2089), 997(331), 1123(373), 6163(2053).
Semiprimes obtained and the corresponding p in the brackets: 5^2(7), 5*41(67), 5*23(37), 11*17(61), 5*11(17), 5*347(577), 17*29(163), 19*43(271), 11*233(853), 13*229(991), 5*239(397), 53*101(1783), 37*241(2971), 11*53(193), 13*151(653), 23*41(313), 5*563(937), 31*43(443).
Numbers divisible by 5 (not semiprimes) obtained and the corresponding p in the brackets: 5^2*37(307), 5^2*109(907), 5^2*487(4057), 5^2*19(157), 5*13*179(3877).
This formula produces 35 primes for the first 55 values of p!
The formula can be extrapolated for all Carmichael numbers and all their prime factors: primes of type 3*p + d  3, where p is a prime factor of a Carmichael number divisible by d; for instance, were obtained the following primes of type 3*p + 10, where p is a prime factor of a Carmichael number divisible by 13: 61, 31, 67, 103, 193, 43, 229, 337, 1201, 79, 211, 823, 607, 463, 1741, 499, 643, 733, 97, 2029, 139, 349, 4129, 6421, 1381, 2731, 1069, 853, 1021, 9421, 5413, 10831, 223, 1933, 8269 (which means 35 primes) for the first 55 values of p!
