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

Author

Harvey P. Dale, Feb 25 2000

Keywords

• easy
• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

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