A090839 Numbers k such that 6*k+1, 6*k+7, 6*k+13, 6*k+19 are consecutive primes.

290, 550, 850, 1060, 2650, 3035, 3245, 5015, 5105, 8935, 10615, 11890, 12925, 13485, 13905, 14850, 15215, 15985, 17560, 17600, 18105, 19925, 20135, 21780, 23510, 24040, 25490, 28830, 31145, 34365, 36355, 38140, 38370, 42025, 43845, 46820, 47575, 48745, 49130, 50495, 53350

Offset

1,1

Comments

All terms are == 0 (mod 5). - Robert G. Wilson v, Dec 12 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

6*290 + 1 = 1741, 6*290 + 7 = 1747, 6*290 + 13 = 1753, 6*290 + 19 = 1759 and 1741, 1747, 1753, 1759 are consecutive primes, so 290 is a term.

Mathematica

Block[{nn = 50500, s}, s = Select[Prime@ Range@ PrimePi[6 (nn + 3) - 1], Divisible[(# + 1), 6] &]; Select[Range@ nn, And[AllTrue[#, PrimeQ], Count[s, q_ /; First[#] < q < Last@ #] == 0] &@ Map[6 # + 1 &, # + Range[0, 3]] &]] (* Michael De Vlieger, Dec 06 2017 *)
fQ[n_] := Block[{p = {6n +1, 6n +7, 6n +13, 6n +19}}, Union@ PrimeQ@ p == {True} && NextPrime[6n +1, 3] == 6n +19]; Select[5 Range@ 10100, fQ] (* Robert G. Wilson v, Dec 12 2017 *)

Prog

(PARI) isok(n) = my(p, q, r); isprime(p=6*n+1) && ((q=6*n+7) == nextprime(p+1)) && ((r=6*n+13) == nextprime(q+1)) && (6*n+19 == nextprime(r+1)); \\ Michel Marcus, Sep 20 2019

Crossrefs

Cf. A033451, A090832, A090833, A090834, A090835, A090836, A090837, A090838.

Sequence in context: A075421 A332229 A296055 * A158255 A295483 A075299

Adjacent sequences: A090836 A090837 A090838 * A090840 A090841 A090842

Keyword

easy,nonn

Author

Pierre CAMI, Dec 09 2003

Extensions

Missing term 5105 and more terms from Michel Marcus, Sep 20 2019

Status

approved