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A245305 Numbers k such that 4k+1, 4k+3, and 6k+5 are all primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A212500 A302198 A279830 * A152450 A059213 A093102

Adjacent sequences:  A245302 A245303 A245304 * A245306 A245307 A245308

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 18 2014

STATUS

approved

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Last modified July 4 17:20 EDT 2022. Contains 355083 sequences. (Running on oeis4.)