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A271080 Integers k such that s(k) = 7523267 + 11184810*k and s(k) + 14 are consecutive primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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?
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
8 is a term because 7523267 + 11184810*8 = 97001747 and 97001761 are consecutive (provable) Sierpiński numbers and they are also consecutive primes.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A157164 A131539 A331419 * A117868 A291001 A062508
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 30 2016
STATUS
approved

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Last modified March 29 06:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)