A361492 Common difference corresponding to increasing arithmetic progression of at least n >= 2 primes whose first term is A284708(n); a(1) = 1.

1, 1, 2, 6, 30, 30, 210, 210, 210, 17430, 30030, 60060, 510510, 3573570

Offset

1,3

Comments

a(22) = 4609098694200 (see Penguin reference).

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

Common difference and corresponding n primes in arithmetic progression.
a(1) = 1: (2);
a(2) = 1: (2, 3);
a(3) = 2: (3, 5, 7);
a(4) = 6: (11, 17, 23, 29);
a(5) = 30: (37, 67, 97, 127, 157);
a(6) = 30: (107, 137, 167, 197, 227, 257);
a(7) = 210: (409, 619, 829, 1039, 1249, 1459, 1669);
a(8) = 210: (409, 619, 829, 1039, 1249, 1459, 1669, 1879);
a(9) = 210: (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(d)); );
a(n) = my(p=2, d); while (!(d=isokp(p, n)), p=nextprime(p+1)); d; \\ Michel Marcus, Mar 16 2023

Crossrefs

Cf. A284708.

Sequence in context: A077634 A095198 A126989 * A128040 A219196 A233358

Adjacent sequences: A361489 A361490 A361491 * A361493 A361494 A361495

Keyword

nonn,more

Author

Bernard Schott, Mar 14 2023

Status

approved