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

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

• nonn

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}.

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

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