%I #26 Feb 07 2019 02:12:09

%S 53,157,173,257,263,373,563,593,607,653,733,947,977,1103,1123,1187,

%T 1223,1367,1747,1753,1907,2287,2417,2677,2903,2963,3307,3313,3637,

%U 3733,4013,4457,4597,4657,4993,5107,5113,5303,5387,5393,5563,5807,6073,6263

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

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

%C Subset of A006489. - _R. J. Mathar_, Apr 11 2008

%C Subset of A006562. - _Zak Seidov_, Feb 14 2013

%C a(n) == {3,7} mod 10. - _Zak Seidov_, Feb 14 2013

%C Minimal difference is 6: a(5) - a(4) = 263 - 257, a(20) - a(19) = 1753 - 1747, ... . - _Zak Seidov_, Feb 14 2013

%H Harvey P. Dale, <a href="/A053070/b053070.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A047948(n) + 6. - _R. J. Mathar_, Apr 11 2008

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

%p 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

%t 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 *)

%t Transpose[Select[Partition[Prime[Range[1000]],3,1],Differences[#]=={6,6}&]][[2]] (* _Harvey P. Dale_, Oct 11 2012 *)

%Y Cf. A047948, A006489, A006562. - _Zak Seidov_, Feb 14 2013

%K easy,nonn

%O 1,1

%A _Harvey P. Dale_, Feb 25 2000

%E Edited by _N. J. A. Sloane_ at the suggestion of _Zak Seidov_, Apr 09 2008