A227281 First primes of arithmetic progressions of 5 primes each with the common difference 30.

7, 11, 37, 107, 137, 151, 277, 359, 389, 401, 541, 557, 571, 877, 1033, 1493, 1663, 2221, 2251, 2879, 3271, 6269, 6673, 6703, 7457, 7487, 9431, 10103, 10133, 10567, 11981, 12457, 12973, 14723, 17047, 19387, 24061, 25643, 25673, 26861, 26891, 27337, 27367

Offset

1,1

Comments

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

For k = 5, we have d = 3# = 6 and there is ONLY one AP-5 with this difference: {5, 11, 17, 23, 29}.

Links

Sameen Ahmed Khan, Table of n, a(n) for n = 1..1184

Example

p = 11 then {11, 11 + 1*30, 11 + 2*30, 11 + 3*30, 11 + 4*30} = {11, 41, 71, 101, 131}, which is 5 primes in arithmetic progression with the difference 5# = 30.

Mathematica

Clear[p]; d = 30; ap5p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d}] == {True, True, True, True, True}, AppendTo[ap5p, p]], {p, 3, 25000, 2}]; ap5p

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227282, A227283, A227284, A227285, A227286.

Sequence in context: A019416 A138122 A176955 * A268579 A129865 A153377

Adjacent sequences: A227278 A227279 A227280 * A227282 A227283 A227284

Keyword

nonn

Author

Sameen Ahmed Khan, Jul 05 2013

Status

approved