A227284 First primes of arithmetic progressions of 9 primes each with the common difference 210.

199, 409, 3499, 10859, 564973, 1288607, 1302281, 2358841, 3600521, 4047803, 17160749, 20751193, 23241473, 44687567, 50655739, 53235151, 87662609, 100174043, 103468003, 110094161, 180885839, 187874017, 192205147, 221712811, 243051733, 243051943, 304570103

Offset

1,1

Comments

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

When a(n+1) = a(n) + 210, as for n = 1, 25, ..., then a(n) is in A094220: start of AP of 10 primes with common distance 210. - M. F. Hasler, Jan 02 2020

Links

Sameen Ahmed Khan, Table of n, a(n) for n = 1..47

OEIS wiki, Primes in arithmetic progression.

Example

p = 409 then the AP-9 is {409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089} with the difference 9# = 2*3*5*7 = 210.

Mathematica

Clear[p]; d = 210; ap9p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d}] == {True, True, True, True, True, True, True, True, True}, AppendTo[ap9p, p]], {p, 3, 10^9, 2}]; ap9p

Prog

(PARI) v=[1..8]*210; forprime(p=1, , for(i=1, #v, isprime(p+v[i])||next(2)); print1(p", ")) \\ M. F. Hasler, Jan 02 2020

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227285, A227286.

Sequence in context: A033168 A227283 A269325 * A140632 A142814 A105975

Adjacent sequences: A227281 A227282 A227283 * A227285 A227286 A227287

Keyword

nonn

Author

Sameen Ahmed Khan, Jul 05 2013

Status

approved