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A053070 Primes n such that n-6, n and n+6 are consecutive primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A044385 A044766 A160058 * 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

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Last modified June 25 12:01 EDT 2017. Contains 288710 sequences.