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 A033447 Initial prime in set of 4 consecutive primes with common difference 12. 23
 111497, 258527, 286777, 318407, 332767, 341827, 358447, 439787, 473887, 480737, 495377, 634187, 647417, 658367, 663857, 703837, 732497, 816317, 819787, 827767, 843067, 862307, 937777, 970457, 970537, 1001267, 1012147, 1032727, 1052707, 1055827, 1104307, 1117877, 1164817, 1165837 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Zak Seidov, Sep 30 2014: (Start) All terms are == {7, 17} mod 30. There is no set of 5 consecutive primes in arithmetic progression with common difference 12 (because a(n)+48 is always divisible by 5). Minimal first difference a(n+1)-a(n) = 40, and this occurs first at a(709) = 26930767, a(11357) = 655389367 and a(23339) = 1510368877; all a(n) are == 7 mod 30. (End) LINKS Zak Seidov, Table of n, a(n) for n = 1..1000 Index entries for sequences related to primes in arithmetic progressions MATHEMATICA A033447 = Reap[For[p = 2, p < 1100000, p = NextPrime[p], p2 = NextPrime[p]; If[p2 - p == 12, p3 = NextPrime[p2]; If[p3 - p2 == 12, p4 = NextPrime[p3]; If[p4 - p3 == 12, Sow[p]]]]]][[2, 1]] (* Jean-François Alcover, Jun 28 2012 *) Transpose[Select[Partition[Prime[Range], 4, 1], Union[ Differences[#]] =={12}&]][] (* Harvey P. Dale, Jun 17 2014 *) PROG (PARI) A033447(n, p=2, show_all=1, g=12, c, o)={forprime(q=p+1, , if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, show_all&& print1(o-g", "); n--||break); o=q-g); o-g} \\ Can be used as next(p)=A033447(1, p+1) to get the next term, e.g.: p=0; A033447_vec=vector(30, i, p=A033447(1, p+1)) \\ M. F. Hasler, Oct 26 2018 CROSSREFS Analogous sequences (start of CPAP-4 with common difference in square brackets): A033451 , this sequence , A033448 , A052242 , A052243 , A058252 , A058323 , A067388 , A259224 , A210683 . Subsequence of A052188 and of A248085. - Zak Seidov, Jun 27 2015 Also subsequence of A054800: start of a CPAP-4, any common difference. Sequence in context: A296370 A206509 A033446 * A203667 A210059 A236892 Adjacent sequences: A033444 A033445 A033446 * A033448 A033449 A033450 KEYWORD nonn AUTHOR Jeff Burch EXTENSIONS More terms from Labos Elemer, Jan 31 2000 Definition clarified by Harvey P. Dale, Jun 17 2014 STATUS approved

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Last modified December 10 18:13 EST 2023. Contains 367717 sequences. (Running on oeis4.)