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A271080 Integers k such that s(k) = 7523267 + 11184810*k and s(k) + 14 are consecutive primes.

%I A271080 #29 Oct 07 2023 18:23:36
%S A271080 8,16,82,101,132,187,201,253,265,300,318,351,393,408,429,449,474,489,
%T A271080 508,660,662,673,687,772,869,877,880,924,945,958,963,984,1028,1042,
%U A271080 1070,1083,1124,1134,1226,1249,1257,1265,1319,1340,1345,1352,1365,1389,1463,1664,1816,1834,1878,1969
%N A271080 Integers k such that s(k) = 7523267 + 11184810*k and s(k) + 14 are consecutive primes.
%C A271080 s(k) and s(k) + 14 are always Sierpiński numbers for k >= 0.
%C A271080 Motivated by the question: What are the consecutive Sierpiński numbers with difference 14 that are also consecutive primes?
%C A271080 See A270971 and A270993 for the reason for the definition's focus on 14.
%C A271080 How does the graph of this sequence look for larger values of n?
%H A271080 Charles R Greathouse IV, <a href="/A271080/b271080.txt">Table of n, a(n) for n = 1..10000</a>
%e A271080 8 is a term because 7523267 + 11184810*8 = 97001747 and 97001761 are consecutive (provable) Sierpiński numbers and they are also consecutive primes.
%t A271080 Select[Range@ 2000, And[PrimeQ@ #, NextPrime@ # == # + 14] &@(7523267 + 11184810 #) &] (* _Michael De Vlieger_, Mar 30 2016 *)
%t A271080 cpQ[n_]:=Module[{c=7523267+11184810n},PrimeQ[c]&&NextPrime[c]==c+14]; Select[Range[ 2000],cpQ] (* _Harvey P. Dale_, Oct 07 2023 *)
%o A271080 (PARI) lista(nn) = for(n=0, nn, if(ispseudoprime(s=7523267 + 11184810*n) && nextprime(s+1) == (s+14), print1(n, ", ")));
%o A271080 (PARI) is(n)=my(s=11184810*n+7523267); isprime(s) && isprime(s+14) && !isprime(s+6) && !isprime(s+12) \\ _Charles R Greathouse IV_, Mar 31 2016
%Y A271080 Cf. A076336, A270971, A270993.
%K A271080 nonn
%O A271080 1,1
%A A271080 _Altug Alkan_, Mar 30 2016