A372042 Monogamously Faithful Primes (primes that are sexy primes with only one other prime in their pair).
83, 89, 131, 137, 191, 193, 197, 199, 223, 229, 307, 311, 313, 317, 331, 337, 383, 389, 433, 439, 443, 449, 457, 461, 463, 467, 503, 509, 541, 547, 571, 577, 677, 683, 751, 757, 821, 823, 827, 829, 853, 857, 859, 863, 877, 881, 883, 887, 991, 997, 1013, 1019, 1033, 1039, 1063, 1069, 1087
Offset: 0
Keywords
Examples
83 and 89 are "sexy" with each other, because they differ by 6. They are monogamously faithful, because neither is sexy with any other number. 71 is not "sexy" because it is not in A136207. 67 is "sexy" with both 61 and 73. Therefore, it is not monogamously faithful, since it has multiple numbers that it is sexy with. 43 is "sexy" only with 37. But it is not monogamously faithful, even though it isn't sexy with another number, because 37 is also "sexy" with 31, therefore "cheating" on 43 with 31.
Programs
-
Maple
isA372042 := proc(n) if isprime(n) then if isprime(n+6) then if not isprime(n-6) and not isprime(n+12) then true; else false; end if; elif isprime(n-6) then if not isprime(n+6) and not isprime(n-12) then true; else false; end if; else false ; end if; else false ; end if; end proc: A372042 := proc(n) option remember; local a; if n = 1 then 83 ; else a := nextprime(procname(n-1)) ; while true do if isA372042(a) then return a; else a := nextprime(a) ; end if; end do: end if; end proc: seq(A372042(n),n=1..80) ; # R. J. Mathar, Jun 10 2024
Comments