A112041 Numbers k such that 1*k + 1, 3*k + 1, 9*k + 1, 27*k + 1 are all primes.

4, 60, 180, 760, 910, 1020, 1230, 1600, 1860, 2160, 2280, 2440, 3850, 5800, 7320, 8680, 12940, 13780, 14740, 17350, 17400, 21840, 22720, 22960, 26040, 27010, 31050, 33870, 34060, 35200, 39900, 40030, 44350, 45280, 45540, 45750, 50460, 52050

Offset

1,1

Comments

Conjecture: all terms except the first are multiples of 10. - Harvey P. Dale, Mar 26 2015

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

1*4 + 1 = 5;
3*4 + 1 = 13;
9*4 + 1 = 37;
27*4 + 1 = 109; 5, 13, 37, 109 are all prime so 4 is in the sequence.

Mathematica

Select[Range[60000], AllTrue[3^Range[0, 3]*#+1, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 26 2015 *)

Prog

(Magma) [n: n in [1..100000] |IsPrime(n+1) and IsPrime(3*n+1) and IsPrime(9*n+1) and IsPrime(27*n+1)] // Vincenzo Librandi, Nov 13 2010

Crossrefs

Cf. A112042, A112043.

Sequence in context: A074835 A060492 A234952 * A210425 A366690 A002060

Adjacent sequences: A112038 A112039 A112040 * A112042 A112043 A112044

Keyword

nonn

Author

Pierre CAMI, Aug 26 2005

Status

approved