A264937 Positive numbers k such that (10^(k+2) - 49) / 3 is prime.

1, 3, 25, 37, 51, 105, 157, 351, 499, 1093, 1987, 8019, 23787, 42795

Offset

1,2

Comments

The numbers that follow the expression in the definition have this form: (3) concatenated k times and prepended to 17.

All terms are odd numbers (if k is even then one can use a^2 - b^2 = (a+b)*(a-b) to get a factorization).

Links

Table of n, a(n) for n=1..14.

Example

3 appears because 33317 ('3' concatenated 3 times and prepended to '17') is prime.

Mathematica

Select[Select[Range[2000], OddQ], PrimeQ[(10^(# + 2) - 49)/3] &] (* or *)
ParallelMap[If[OddQ[#] && PrimeQ[(10^(# + 2) - 49)/3], #, Nothing] &, Range[2000]]

Prog

(Magma) [n: n in [1..400]| IsPrime((10^(n+2) - 49) div 3)]; // Vincenzo Librandi, Nov 29 2015
(PARI) is(n)=ispseudoprime((10^(n+2)-49)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Sequence in context: A129599 A042899 A266702 * A354725 A051280 A145609

Adjacent sequences: A264934 A264935 A264936 * A264938 A264939 A264940

Keyword

nonn,base,hard,more

Author

Mikk Heidemaa, Nov 28 2015

Extensions

a(13)-a(14) by Mikk Heidemaa, Apr 28 2017

Status

approved