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
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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 *) Select[(#-1)/6&/@Select[Partition[Prime[Range[30000]],4,1],Differences[#]=={6,6,6}&][[;;,1]],IntegerQ] (* Harvey P. Dale, Apr 05 2025 *) -
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
Extensions
Missing term 5105 and more terms from Michel Marcus, Sep 20 2019
Comments