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 A033451 Initial prime in set of 4 consecutive primes with common difference 6. 51
 251, 1741, 3301, 5101, 5381, 6311, 6361, 12641, 13451, 14741, 15791, 15901, 17471, 18211, 19471, 23321, 26171, 30091, 30631, 53611, 56081, 62201, 63691, 71341, 75521, 77551, 78791, 80911, 82781, 83431, 84431, 89101, 89381, 91291, 94421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes p such that p, p+6, p+12, p+18 are consecutive primes. It is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression. As of March 2013 the record is 10 primes. Note that the Green and Tao reference is about arithmetic progressions that are not necessarily consecutive. - Michael B. Porter, Mar 05 2013 Subsequence of A023271. - R. J. Mathar, Nov 04 2006 All terms p == 1(mod 10) and hence p+24 are always divisible by 5. - Zak Seidov, Jun 20 2015 Subsequence of A054800, with which is coincides up to a(24), but a(25) = A054800(26). - M. F. Hasler, Oct 26 2018 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Jens Kruse Andersen, The Largest Known CPAP's Ben Green and Terence Tao, The primes contain arbitrarily long arithmetic progressions, arXiv:math/0404188 [math.NT], 2004-2007. B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167(2008), 481-547. FORMULA a(n) = A000040(A090832(n)). - Zak Seidov, Jun 20 2015 EXAMPLE 251, 257, 263, 269 are consecutive primes: 257 = 251 + 6, 263 = 251 + 12, 269 = 251 + 18. MAPLE N:=10^5: # to get all terms <= N. Primes:=select(isprime, [seq(i, i=3..N+18, 2)]): Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1], Primes[t+3]-Primes[t+2]]=[6, 6, 6], [\$1..nops(Primes)-3])]; # Muniru A Asiru, Aug 04 2017 MATHEMATICA A033451 = Reap[ For[p = 2, p < 100000, p = NextPrime[p], p2 = NextPrime[p]; If[p2 - p == 6, p3 = NextPrime[p2]; If[p3 - p2 == 6, p4 = NextPrime[p3]; If[p4 - p3 == 6, Sow[p]]]]]][[2, 1]] (* Jean-François Alcover, Jun 28 2012 *) Transpose[Select[Partition[Prime[Range[16000]], 4, 1], Union[ Differences[ #]] == {6}&]][[1]] (* Harvey P. Dale, Jun 17 2014 *) PROG (PARI) p=2; q=3; r=5; forprime(s=7, 1e4, if(s-p==18 && s-q==12 && s-r==6, print1(p", ")); p=q; q=r; r=s) \\ Charles R Greathouse IV, Feb 14 2013 CROSSREFS Intersection of A054800 and A023271. Cf. A090832, A090833, A090834, A090835, A090836, A090837, A090838, A090839. Analogous sequences [with common difference in square brackets]: A033447 [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388[48]. Cf. A058362, A059044. Subsequence of A047948. Sequence in context: A215607 A099734 A054800 * A201793 A183840 A234929 Adjacent sequences:  A033448 A033449 A033450 * A033452 A033453 A033454 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)