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

Author

Altug Alkan, Mar 30 2016

Keywords

• nonn

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?

Examples

			8 is a term because 7523267 + 11184810*8 = 97001747 and 97001761 are consecutive (provable) Sierpiński numbers and they are also consecutive primes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076336, A270971, A270993.

Programs

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 *)

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