A284708 Smallest initial prime p for at least n primes in increasing arithmetic progression with a common difference less than p.

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.

Links

Table of n, a(n) for n=1..14.

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.

Cf. A123556, A342309.

Sequence in context: A157301 A143931 A143933 * A265783 A246670 A075095

Adjacent sequences: A284705 A284706 A284707 * A284709 A284710 A284711

Keyword

nonn,more

Author

Arkadiusz Wesolowski, Jan 09 2018

Extensions

Name edited by Bernard Schott, Mar 15 2023

Status

approved