A084696 Beginning with 3, primes such that a(2n) = {a(2n-1) +a(2n+1)}/2.

3, 5, 7, 13, 19, 31, 43, 61, 79, 103, 127, 139, 151, 157, 163, 181, 199, 211, 223, 277, 331, 349, 367, 373, 379, 409, 439, 463, 487, 547, 607, 613, 619, 631, 643, 691, 739, 811, 883, 937, 991, 1021, 1051, 1069, 1087, 1129, 1171, 1201, 1231, 1279, 1327, 1399

Offset

1,1

Comments

For n > 1, a(2n) = smallest prime of the form a(2n-1) + 6k where a(2n-1) + 12k is also a prime and is equal to a(2n+1). The difference of successive terms is 2,2,6,6,12,12,18,18,24,24,12,12,6,6,18,18,...

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

f[l_List] := Block[{p = Last[l], k = 2, t}, While[t = {p + k, p + 2k}; ! And @@ PrimeQ /@ t, k += 2 ]; Join[l, t]]; Nest[f, {3}, 26] (* Ray Chandler, Sep 29 2006 *)

Crossrefs

A122809 gives bisection of first difference/2 of this sequence.

Sequence in context: A184248 A206023 A067829 * A352952 A354219 A330222

Adjacent sequences: A084693 A084694 A084695 * A084697 A084698 A084699

Keyword

nonn

Author

Amarnath Murthy, Jun 05 2003

Extensions

More terms from David Wasserman, Dec 30 2004

Status

approved