The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A338270 Primes p such that the sum of p and the average of the primes immediately before and after p is prime. 2
 23, 37, 79, 83, 89, 131, 233, 359, 367, 379, 439, 443, 509, 661, 683, 727, 809, 997, 1013, 1237, 1297, 1319, 1381, 1439, 1499, 1543, 1559, 1601, 1657, 1789, 1811, 1867, 1889, 2011, 2081, 2111, 2137, 2161, 2281, 2351, 2393, 2399, 2467, 2543, 2579, 2693, 2699, 2789, 2851, 2939, 3169, 3181, 3187 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS At least one of the prime gaps before and after a(n) is divisible by 6, and exactly one is divisible by 4. Dickson's conjecture implies there are, for example, infinitely many primes p such that p-4 is the prime before p, p+6 is the prime after p, and 2*p+1 is prime; these are members of the sequence. For the sum of a(n) and the average of the primes immediately before and after a(n) see A338273. a(3)=79, a(4)=83, a(5)=89 are three consecutive primes.  The first case of four consecutive primes in the sequence is a(723)=67789, a(724)=67801, a(725)=67807, a(726)=67819.  The first case of five consecutive primes in the sequence is a(13175)=2263249, a(13176)=2263273, a(13177)=2263307, a(13178)=2263319, a(13179)=2263321. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(3)=79 is in the sequence because 79 is prime, the primes before and after 79 are 73 and 83, and 79 + (73+83)/2 = 157 is prime. MAPLE q:= 3: r:= 5: count:= 0: R:= NULL: while count < 100 do p:= q; q:= r; r:= nextprime(r); if isprime((p+2*q+r)/2) then count:= count+1; R:= R, q; fi od: R; CROSSREFS Cf. A338273. Sequence in context: A089685 A186883 A068016 * A140442 A078731 A133957 Adjacent sequences:  A338267 A338268 A338269 * A338271 A338272 A338273 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Oct 19 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 4 19:28 EDT 2022. Contains 355084 sequences. (Running on oeis4.)