

A112041


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


3



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
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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 A002060 A247739
Adjacent sequences: A112038 A112039 A112040 * A112042 A112043 A112044


KEYWORD

nonn


AUTHOR

Pierre CAMI, Aug 26 2005


STATUS

approved



