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A372042 Monogamously Faithful Primes (primes that are sexy primes with only one other prime in their pair).

%I A372042 #11 Jun 28 2024 23:13:23
%S A372042 83,89,131,137,191,193,197,199,223,229,307,311,313,317,331,337,383,
%T A372042 389,433,439,443,449,457,461,463,467,503,509,541,547,571,577,677,683,
%U A372042 751,757,821,823,827,829,853,857,859,863,877,881,883,887,991,997,1013,1019,1033,1039,1063,1069,1087
%N A372042 Monogamously Faithful Primes (primes that are sexy primes with only one other prime in their pair).
%C A372042 These are all the numbers found in A136207 but not found in A046118, A046119, A046120, A023271, A046122, A046123, or A046124, i.e., members of a sexy prime pair but not members of sexy prime triplets, quadruplets, ...
%e A372042 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.
%e A372042 71 is not "sexy" because it is not in A136207.
%e A372042 67 is "sexy" with both 61 and 73. Therefore, it is not monogamously faithful, since it has multiple numbers that it is sexy with.
%e A372042 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.
%p A372042 isA372042 := proc(n)
%p A372042     if isprime(n) then
%p A372042         if isprime(n+6) then
%p A372042             if not isprime(n-6) and not isprime(n+12) then
%p A372042                 true;
%p A372042             else
%p A372042                 false;
%p A372042             end if;
%p A372042         elif isprime(n-6) then
%p A372042             if not isprime(n+6) and not isprime(n-12) then
%p A372042                 true;
%p A372042             else
%p A372042                 false;
%p A372042             end if;
%p A372042         else
%p A372042             false ;
%p A372042         end if;
%p A372042     else
%p A372042         false ;
%p A372042     end if;
%p A372042 end proc:
%p A372042 A372042 := proc(n)
%p A372042     option remember;
%p A372042     local a;
%p A372042     if n = 1 then
%p A372042         83 ;
%p A372042     else
%p A372042         a := nextprime(procname(n-1)) ;
%p A372042         while true do
%p A372042             if isA372042(a) then
%p A372042                 return a;
%p A372042             else
%p A372042                 a := nextprime(a) ;
%p A372042             end if;
%p A372042         end do:
%p A372042     end if;
%p A372042 end proc:
%p A372042 seq(A372042(n),n=1..80) ; # _R. J. Mathar_, Jun 10 2024
%Y A372042 Cf. A136207, A046117, A046118, A046119, A046120, A023271, A046122, A046123, A046124.
%K A372042 nonn
%O A372042 0,1
%A A372042 _Ryan Stoler_, Apr 17 2024