The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A354377 Initial terms associated with the arithmetic progressions of primes of A354376. 5
 2, 2, 3, 7, 5, 7, 7, 881, 3499, 199, 75307, 110437, 4943, 31385539, 115453391, 53297929, 3430751869, 4808316343, 8297644387, 214861583621, 5749146449311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently: Let i, i+d, i+2d, ..., i+(n-1)d be an arithmetic progression of exactly n primes; choose the one which minimizes the last term; then a(n) = first term i. The adverb "exactly" requires both i-d and i+n*d to be nonprime (see A113827). For the corresponding values of the last term, see A354376. The primes in these arithmetic progressions need not be consecutive. (The smallest prime at the start of a run of exactly n consecutive primes in arithmetic progression is A006560(n).) a(n) != A113827(n) for n = 4, 8, 9, 11. - Michael S. Branicky, May 26 2022 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, A5, Arithmetic progressions of primes. LINKS Table of n, a(n) for n=1..21. EXAMPLE The first few corresponding arithmetic progressions are: n = 1 (2); n = 2 (2, 3); n = 3 (3, 5, 7); n = 4 (7, 19, 31, 43); n = 5 (5, 11, 17, 23, 29); n = 6 (7, 37, 67, 97, 127, 157); n = 7 (7, 157, 307, 457, 607, 757, 907)... CROSSREFS Cf. A006560, A113827, A354376. Sequence in context: A267822 A210598 A330728 * A051301 A002583 A068519 Adjacent sequences: A354374 A354375 A354376 * A354378 A354379 A354380 KEYWORD nonn,more AUTHOR Bernard Schott, May 26 2022 EXTENSIONS a(8)-a(21) from Michael S. Branicky, May 26 2022 STATUS approved

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

Last modified April 22 22:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)