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A271080
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Integers k such that s(k) = 7523267 + 11184810*k and s(k) + 14 are consecutive primes.
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1
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8, 16, 82, 101, 132, 187, 201, 253, 265, 300, 318, 351, 393, 408, 429, 449, 474, 489, 508, 660, 662, 673, 687, 772, 869, 877, 880, 924, 945, 958, 963, 984, 1028, 1042, 1070, 1083, 1124, 1134, 1226, 1249, 1257, 1265, 1319, 1340, 1345, 1352, 1365, 1389, 1463, 1664, 1816, 1834, 1878, 1969
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OFFSET
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1,1
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COMMENTS
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s(k) and s(k) + 14 are always Sierpiński numbers for k >= 0.
Motivated by the question: What are the consecutive Sierpiński numbers with difference 14 that are also consecutive primes?
See A270971 and A270993 for the reason for the definition's focus on 14.
How does the graph of this sequence look for larger values of n?
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LINKS
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EXAMPLE
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8 is a term because 7523267 + 11184810*8 = 97001747 and 97001761 are consecutive (provable) Sierpiński numbers and they are also consecutive primes.
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MATHEMATICA
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Select[Range@ 2000, And[PrimeQ@ #, NextPrime@ # == # + 14] &@(7523267 + 11184810 #) &] (* Michael De Vlieger, Mar 30 2016 *)
cpQ[n_]:=Module[{c=7523267+11184810n}, PrimeQ[c]&&NextPrime[c]==c+14]; Select[Range[ 2000], cpQ] (* Harvey P. Dale, Oct 07 2023 *)
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PROG
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(PARI) lista(nn) = for(n=0, nn, if(ispseudoprime(s=7523267 + 11184810*n) && nextprime(s+1) == (s+14), print1(n, ", ")));
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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