A006489 Numbers k such that k-6, k, and k+6 are primes.

11, 13, 17, 23, 37, 47, 53, 67, 73, 103, 107, 157, 173, 233, 257, 263, 277, 353, 373, 563, 593, 607, 613, 647, 653, 733, 947, 977, 1097, 1103, 1123, 1187, 1223, 1283, 1297, 1367, 1433, 1453, 1487, 1493, 1607, 1613, 1663, 1747, 1753, 1783, 1867, 1873

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

A006562 without the first term 5 is a subsequence. - Zak Seidov, Apr 19 2021

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Joseph Hirsch, Prime Triplets, Mathematics Teacher, 62 (1969), 467ff (see p. 471).
• D. S. Kluk and N. J. A. Sloane, Correspondence, 1979

Crossrefs

Subsequence of A023201.

Cf. A006562.

Programs

Haskell

a006489 n = a006489_list !! (n-1)
a006489_list = filter
   ((== 1) . a010051 . (subtract 6)) $ dropWhile (<= 6) a023201_list
-- Reinhard Zumkeller, Feb 25 2013

Mathematica

Select[Prime[Range[300]],And@@PrimeQ[#+{6,-6}]&] (* Harvey P. Dale, May 21 2012 *)

PARI

is(n)=isprime(n-6) && isprime(n) && isprime(n+6) \\ Charles R Greathouse IV, Feb 07 2017

Extensions

More terms from James Sellers, Dec 24 1999