A227282 First primes of arithmetic progressions of 7 primes each with the common difference 210.

47, 179, 199, 409, 619, 829, 881, 1091, 1453, 3499, 3709, 3919, 10529, 10627, 10837, 10859, 11069, 11279, 14423, 20771, 22697, 30097, 30307, 31583, 31793, 32363, 41669, 75703, 93281, 95747, 120661, 120737, 120871, 120947, 129287, 140603, 153319, 153529

Offset

1,1

Comments

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

For k = 7, we have d = 5*5# = 150 and there is ONLY one AP-7 with this difference: {7, 157, 307, 457, 607, 757, 907}.

Links

Sameen Ahmed Khan and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 2484 terms from Khan)

Example

p = 179 then the AP-5 is {179, 389, 599, 809, 1019, 1229, 1439} with the difference 7# = 210.

Mathematica

Clear[p]; d = 210; ap7p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d}] == {True, True, True, True, True, True, True}, AppendTo[ap7p, p]], {p, 3, 10^9, 2}]; ap7p
Select[Prime[Range[15000]], And@@PrimeQ[NestList[210+#&, #, 6]]&] (* Harvey P. Dale, Nov 16 2013 *)

Prog

(PARI) is(p)=forstep(k=p, p+1260, 210, if(!isprime(k), return(0))); 1 \\ Charles R Greathouse IV, Dec 19 2013

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227283, A227284, A227285, A227286.

Sequence in context: A142916 A253351 A253344 * A204610 A158632 A142413

Adjacent sequences: A227279 A227280 A227281 * A227283 A227284 A227285

Keyword

nonn

Author

Sameen Ahmed Khan, Jul 05 2013

Status

approved