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A284708
Smallest initial prime p for at least n primes in increasing arithmetic progression with a common difference less than p.
1
2, 2, 3, 11, 37, 107, 409, 409, 409, 25471, 53173, 65003, 766439, 11797483
OFFSET
1,1
COMMENTS
Conjecture: a(n) > A034386(n) for every n >= 4.
From Bernard Schott, Mar 15 2023: (Start)
Corresponding common differences are in A361492.
a(22) = 11410337850553 since it is the smallest term in a sequence of 22 primes in arithmetic progression, and the corresponding common difference 4609098694200 is < a(22) (see Penguin reference). (End)
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, entry 11410337850553, page 191.
EXAMPLE
Smallest initial prime p, primes in arithmetic progression:
a(1) = 2: (2);
a(2) = 2: (2, 3);
a(3) = 3: (3, 5, 7);
a(4) = 11: (11, 17, 23, 29);
a(5) = 37: (37, 67, 97, 127, 157);
a(6) = 107: (107, 137, 167, 197, 227, 257);
a(7) = 409: (409, 619, 829, 1039, 1249, 1459, 1669);
a(8) = 409: (409, 619, 829, 1039, 1249, 1459, 1669, 1879);
a(9) = 409: (409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089);
PROG
(PARI) isokd(p, n, d) = for (i=1, n, if (!isprime(p+(i-1)*d), return(0))); 1;
isokp(p, n) = for (d=1, p-1, if (isokd(p, n, d), return(1)); );
a(n) = my(p=2); while (!isokp(p, n), p=nextprime(p+1)); p; \\ Michel Marcus, Mar 15 2023
CROSSREFS
Cf. A361492.
Sequence in context: A157301 A143931 A143933 * A265783 A246670 A075095
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
Name edited by Bernard Schott, Mar 15 2023
STATUS
approved