This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006560 Smallest starting prime for n consecutive primes in arithmetic progression. (Formerly M0927) 9
 2, 2, 3, 251, 9843019, 121174811 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The primes following a(5) and a(6) occur at a(n)+30*k, k=0..(n-1). a(6) was found by Lander and Parkin. The next term requires a spacing >= 210. The expected size is a(7) > 10^21 (see link). - Hugo Pfoertner, Jun 25 2004 From Daniel Forgues, Jan 17 2011: (Start) It is conjectured that there are arithmetic progressions of n consecutive primes for any n. Common differences of first and smallest AP of n >= 1 consecutive primes: {0, 1, 2, 6, 30, 30, >= 210, >= 210, >= 210, >= 210, >= 2310, ...} (End) a(7) <= 382003672700092872707633, found by P. Zimmermann, cf. J. K. Andersen link. - M. F. Hasler, Oct 26 2018 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Jens Kruse Andersen, The smallest known CPAP-k. Chris K. Caldwell, Consecutive Primes in Arithmetic Progression Harvey Dubner and Harry Nelson, Seven consecutive primes in arithmetic progression, Math. Comp., 66 (1997) 1743-1749. MR 98a:11122. H. Dubner, T. Forbes, N. Lygeros, M. Mizony, H. Nelson, P. Zimmermann, Ten consecutive primes in arithmetic progression, Math. Comp., Vol. 71, No. 239 (2002) 1323-1328. Daniel Forgues, Wiki about consecutive primes in arithmetic progression. L. J. Lander and T. R. Parkin, Consecutive primes in arithmetic progression, Math. Comp., Vol. 21, No. 99 (1967) p 489. Manfred Toplic, The nine and ten primes project, 2004. FORMULA a(n) = A000040(A089180(n)), or A089180(n) = A000720(a(n)). - M. F. Hasler, Oct 27 2018 EXAMPLE First and smallest occurrence of n, n >= 1, consecutive primes in arithmetic progression: a(1) = 2: (2) (degenerate arithmetic progression); a(2) = 2: (2, 3) (degenerate arithmetic progression); a(3) = 3: (3, 5, 7); a(4) = 251: (251, 257, 263, 269); a(5) = 9843019: (9843019, 9843049, 9843079, 9843109, 9843139); a(6) = 121174811: (121174811, 121174841, 121174871, 121174901, 121174931, 121174961); MATHEMATICA Join[{2}, Table[SelectFirst[Partition[Prime[Range[691*10^4]], n, 1], Length[ Union[ Differences[ #]]] == 1&][[1]], {n, 2, 6}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 10 2019 *) CROSSREFS Cf. A005115, A006562, A093364, A126989. a(5) corresponds to A052243(20) followed by A052243(21) 9843049. Cf. A089180: indices primes a(n). Cf. A054800: start of 4 consecutive primes in arithmetic progression (CPAP-4), A033451: start of CPAP-4 with common difference 6, A052239: start of first CPAP-4 with common difference 6n. Cf. A059044: start of 5 consecutive primes in arithmetic progression, A210727: CPAP-5 with common difference 60. Cf. A058362: start of 6 consecutive primes in arithmetic progression. Sequence in context: A177764 A027498 A094877 * A088251 A229627 A140839 Adjacent sequences:  A006557 A006558 A006559 * A006561 A006562 A006563 KEYWORD nonn,hard,nice AUTHOR EXTENSIONS Edited by Daniel Forgues, Jan 17 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)