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A047948
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Smallest of three consecutive primes with a difference of 6: primes p such that p+6 and p+12 are the next two primes.
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19
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47, 151, 167, 251, 257, 367, 557, 587, 601, 647, 727, 941, 971, 1097, 1117, 1181, 1217, 1361, 1741, 1747, 1901, 2281, 2411, 2671, 2897, 2957, 3301, 3307, 3631, 3727, 4007, 4451, 4591, 4651, 4987, 5101, 5107, 5297, 5381, 5387, 5557, 5801, 6067, 6257, 6311
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| Let p(k) = k-th prime; sequence gives n such that p(n+2)-p(n+1)=p(n+1)-p(n)=6.
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EXAMPLE
| 47 is a term as the next two primes are 53 and 59.
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MATHEMATICA
| ok[p_] := (q = NextPrime[p]) == p+6 && NextPrime[q] == q+6; Select[Prime /@ Range[1000], ok][[;; 45]] (* From Jean-François Alcover, Jul 11 2011 *)
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PROG
| (PARI) is(n)=isprime(n+6)&&isprime(n+12)&&!isprime(n+2)&&!isprime(n+4)&&!isprime(n+8)&&!isprime(n+10)&&isprime(n) \\ Charles R Greathouse IV, Aug 17 2011
(PARI) p=2; q=3; forprime(r=5, 1e4, if(r-p==12&&q-p==6, print1(p", ")); p=q; q=r) \\ Charles R Greathouse IV, Aug 17 2011
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CROSSREFS
| Cf. A031924, A046138, A046789.
Cf. A033451 (four consecutive primes with difference 6)
Sequence in context: A044379 A044760 A142505 * A142529 A142634 A140641
Adjacent sequences: A047945 A047946 A047947 * A047949 A047950 A047951
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Enoch Haga (Enokh(AT)comcast.net)
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EXTENSIONS
| Corrected by T. D. Noe, Mar 07 2008
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