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A227284 First primes of arithmetic progressions of 9 primes each with the common difference 210. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 15:36 EST 2021. Contains 349394 sequences. (Running on oeis4.)