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%I A266163 #19 Sep 08 2022 08:46:15
%S A266163 467,2179,2777,4877,6151,6173,6871,7907,7937,8329,9791,11261,11287,
%T A266163 12119,12227,12941,13009,14657,14831,15061,15607,16127,16193,16453,
%U A266163 16787,16831,17989,18701,18803,18947,19507,20483,20521,20627,22291,22397,22409,22877,23497
%N A266163 Primes prime(k) such that (prime(k)*prime(k+1)+1)/2 is prime.
%C A266163 22397 and 22409 are first consecutive primes in this sequence. - _Altug Alkan_, Dec 22 2015
%C A266163 The next consecutive primes in this sequence are 134093 and 134129, 405541 and 405553, 432073 and 432097, 480803 and 480827, 586213 and 586237, ... - _Harvey P. Dale_, Dec 25 2015
%H A266163 Robert Israel, <a href="/A266163/b266163.txt">Table of n, a(n) for n = 1..10000</a>
%p A266163 lastp:= 3:
%p A266163 count:= 0:
%p A266163 while count < 100 do
%p A266163   p:= nextprime(lastp);
%p A266163   if isprime((lastp*p+1)/2) then
%p A266163     count:= count+1;
%p A266163     A[count]:= lastp;
%p A266163   fi;
%p A266163   lastp:= p;
%p A266163 od:
%p A266163 seq(A[i],i=1..100);
%t A266163 Prime@ Select[Range@ 2620, PrimeQ[(Prime@ # Prime[# + 1] + 1)/2] &] (* _Michael De Vlieger_, Dec 22 2015 *)
%t A266163 Transpose[Select[Partition[Prime[Range[50000]],2,1],PrimeQ[ (Times@@#+1)/2]&]] [[1]] (* _Harvey P. Dale_, Dec 25 2015 *)
%o A266163 (PARI) lista(nn) = {forprime(p=3, nn, if(ispseudoprime((p*nextprime(p+1)+1)/2), print1(p, ", ")));} \\ _Altug Alkan_, Dec 22 2015
%o A266163 (Magma) [p: p in PrimesInInterval(3,3*10^4) | IsPrime((p*NextPrime(p+1)+1) div 2)]; // _Vincenzo Librandi_, Dec 23 2015
%Y A266163 Cf. A023524.
%K A266163 nonn
%O A266163 1,1
%A A266163 _Robert Israel_, Dec 22 2015

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