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%I #11 Mar 13 2023 06:00:58
%S 4363,13729,31607,6973007,208969199
%N Primes p followed by two or more 2-pseudoprimes (A001567) before the next prime.
%C Is this sequence infinite? Is there a prime followed by three pseudoprimes before the next prime? I believe heuristics suggest "no" to both.
%C From _Amiram Eldar_, Mar 12 2023: (Start)
%C The primes preceding the terms of A335326.
%C There are no more terms below 2^64. (End)
%e a(n): pseudoprimes following a(n)
%e 4363: 4369, 4371
%e 13729: 13741, 13747
%e 31607: 31609, 31621
%e 6973007: 6973057, 6973063
%e 208969199: 208969201, 208969223
%o (PARI) prp(n,a=2)=Mod(a,n)^(n-1)==1
%o list(lim)=my(v=List(),p=3); forprime(q=5,lim, my(s=0); forstep(k=p+2,q-2,2, if(prp(k) && s++>1, listput(v,p))); p=q); Vec(v)
%Y Cf. A001567, A335326.
%K nonn,more
%O 1,1
%A _Charles R Greathouse IV_, Mar 07 2023
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