A053070 Primes p such that p-6, p and p+6 are consecutive primes.

53, 157, 173, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1747, 1753, 1907, 2287, 2417, 2677, 2903, 2963, 3307, 3313, 3637, 3733, 4013, 4457, 4597, 4657, 4993, 5107, 5113, 5303, 5387, 5393, 5563, 5807, 6073, 6263

Offset

1,1

Comments

Balanced primes separated from the next lower and next higher prime neighbors by 6.

Subset of A006489. - R. J. Mathar, Apr 11 2008

Subset of A006562. - Zak Seidov, Feb 14 2013

a(n) == {3,7} mod 10. - Zak Seidov, Feb 14 2013

Minimal difference is 6: a(5) - a(4) = 263 - 257, a(20) - a(19) = 1753 - 1747, ... . - Zak Seidov, Feb 14 2013

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A047948(n) + 6. - R. J. Mathar, Apr 11 2008

Example

157 is separated from both the next lower prime, 151 and the next higher prime, 163, by 6.

Maple

for i from 1 by 1 to 800 do if ithprime(i+1) = ithprime(i) + 6 and ithprime(i+2) = ithprime(i) + 12 then print(ithprime(i+1)); fi; od; # Zerinvary Lajos, Apr 27 2007

Mathematica

lst={}; Do[p=Prime[n]; If[p-Prime[n-1]==Prime[n+1]-p==6, AppendTo[lst, p]], {n, 2, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 20 2010 *)
Transpose[Select[Partition[Prime[Range[1000]], 3, 1], Differences[#]=={6, 6}&]][[2]] (* Harvey P. Dale, Oct 11 2012 *)

Crossrefs

Cf. A047948, A006489, A006562. - Zak Seidov, Feb 14 2013

Sequence in context: A342450 A160058 A353136 * A140655 A142508 A279259

Adjacent sequences: A053067 A053068 A053069 * A053071 A053072 A053073

Keyword

easy,nonn

Author

Harvey P. Dale, Feb 25 2000

Extensions

Edited by N. J. A. Sloane at the suggestion of Zak Seidov, Apr 09 2008

Status

approved