

A271080


Integers n such that s(n) = 7523267 + 11184810*n and s(n) + 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
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OFFSET

1,1


COMMENTS

s(n) and s(n) + 14 are always Sierpiński numbers for n >= 0.
Motivation was the this question: What are the consecutive Sierpiński numbers with 14 difference that are also consecutive primes?
See A270971 and A270993 for the reason of "14" that definition focuses on.
How is the graph of this sequence 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 *)


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



