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

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

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

Cf. A076336, A270971, A270993.

Sequence in context: A157164 A131539 A331419 * A117868 A291001 A062508

Adjacent sequences: A271077 A271078 A271079 * A271081 A271082 A271083

Keyword

nonn

Author

Altug Alkan, Mar 30 2016

Status

approved