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A227282 First primes of arithmetic progressions of 7 primes each with the common difference 210. 6
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 (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.

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

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Last modified June 27 17:44 EDT 2017. Contains 288790 sequences.