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Monogamously Faithful Primes (primes that are sexy primes with only one other prime in their pair).
1

%I #11 Jun 28 2024 23:13:23

%S 83,89,131,137,191,193,197,199,223,229,307,311,313,317,331,337,383,

%T 389,433,439,443,449,457,461,463,467,503,509,541,547,571,577,677,683,

%U 751,757,821,823,827,829,853,857,859,863,877,881,883,887,991,997,1013,1019,1033,1039,1063,1069,1087

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

%C 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 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 71 is not "sexy" because it is not in A136207.

%e 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 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 isA372042 := proc(n)

%p if isprime(n) then

%p if isprime(n+6) then

%p if not isprime(n-6) and not isprime(n+12) then

%p true;

%p else

%p false;

%p end if;

%p elif isprime(n-6) then

%p if not isprime(n+6) and not isprime(n-12) then

%p true;

%p else

%p false;

%p end if;

%p else

%p false ;

%p end if;

%p else

%p false ;

%p end if;

%p end proc:

%p A372042 := proc(n)

%p option remember;

%p local a;

%p if n = 1 then

%p 83 ;

%p else

%p a := nextprime(procname(n-1)) ;

%p while true do

%p if isA372042(a) then

%p return a;

%p else

%p a := nextprime(a) ;

%p end if;

%p end do:

%p end if;

%p end proc:

%p seq(A372042(n),n=1..80) ; # _R. J. Mathar_, Jun 10 2024

%Y Cf. A136207, A046117, A046118, A046119, A046120, A023271, A046122, A046123, A046124.

%K nonn

%O 0,1

%A _Ryan Stoler_, Apr 17 2024