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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
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
Sequence in context: A267822 A210598 A330728 * A051301 A002583 A068519
KEYWORD
nonn,more
AUTHOR
Bernard Schott, May 26 2022
EXTENSIONS
a(8)-a(21) from Michael S. Branicky, May 26 2022
STATUS
approved

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