A245305 Numbers k such that 4k+1, 4k+3, and 6k+5 are all primes.

1, 4, 7, 37, 142, 154, 202, 214, 307, 424, 469, 487, 499, 559, 577, 664, 742, 814, 847, 979, 982, 1054, 1129, 1159, 1162, 1252, 1369, 1522, 1612, 1642, 1672, 1837, 1987, 2107, 2134, 2149, 2209, 2242, 2359, 2407, 2419, 2482, 2632, 2677, 2767, 2887, 2929, 2944

Offset

1,2

Comments

Sequence is infinite (Sierpiński).

Infinitude of the sequence would follow from Dickson's (unproved) conjecture. - Jens Kruse Andersen, Jul 18 2014

References

W. Sierpiński, A Selection of Problems in the Theory of Numbers. Pergamon, 1964, p. 52, #15.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Mathematica

Select[Range[0, 3000], PrimeQ[4 # + 1] && PrimeQ[4 # + 3] && PrimeQ[6 # + 5] &] (* Vincenzo Librandi, Jun 15 2015 *)

Prog

(Haskell)
a245305 n = a245305_list !! (n-1)
a245305_list = map ((`div` 4) . (subtract 1) . head) $
   filter (all (== 1) . map a010051') $
          iterate (zipWith (+) [4, 4, 6]) [1, 3, 5]
(Magma) [n: n in [0..3*10^3] | IsPrime(4*n+1) and IsPrime(4*n+3) and IsPrime(6*n+5)]; // Vincenzo Librandi, Jun 15 2015
(PARI) isok(k) = isprime(4*k+1) && isprime(4*k+3) && isprime(6*k+5); \\ Michel Marcus, Jan 24 2022

Crossrefs

Cf. A010051, A007811, A125855, A245304.

Sequence in context: A302198 A279830 A367775 * A152450 A059213 A093102

Adjacent sequences: A245302 A245303 A245304 * A245306 A245307 A245308

Keyword

nonn

Author

Reinhard Zumkeller, Jul 18 2014

Status

approved