A039949 Primes of the form 30n - 13.

17, 47, 107, 137, 167, 197, 227, 257, 317, 347, 467, 557, 587, 617, 647, 677, 797, 827, 857, 887, 947, 977, 1097, 1187, 1217, 1277, 1307, 1367, 1427, 1487, 1607, 1637, 1667, 1697, 1787, 1847, 1877, 1907, 1997, 2027, 2087, 2207, 2237, 2267, 2297, 2357, 2417

Offset: 1

Author

Felice Russo

Keywords

• nonn
• easy

Comments

This linear form produces the most primes for n between 1 and 1000 (411/1000).

Primes congruent to 17 (mod 30). - Omar E. Pol, Aug 15 2007

Primes ending in 7 with (SOD-1)/3 non-integer where SOD is sum of digits. - Ki Punches

Or primes p such that (p mod 3) = (p mod 5) and (p mod 2) <> (p mod 3), (p > 2). - Mikk Heidemaa, Jan 19 2016

References

• C. Clawson, Mathematical Mysteries, Plenum Press, 1996, p. 173

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A132230-A132236, A141860.

Programs

Magma

[p: p in PrimesUpTo(3000) | p mod 30 in [17]]; // Vincenzo Librandi, Aug 04 2012

Mathematica

Select[Prime[Range[1000]],MemberQ[{17},Mod[#,30]]&] (* Vincenzo Librandi, Aug 04 2012 *)
Select[Range[17,3000,30],PrimeQ] (* Zak Seidov, Apr 15 2015 *)

PARI

select(n->n%30==17, primes(500)) \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = A158648(n)*30 + 17. - Ray Chandler, Apr 07 2009

Intersection of A030432 and A007528. - Ray Chandler, Apr 07 2009

a(n) = A141860(n+1). - Zak Seidov, Apr 15 2015

Extensions

Extended by Ray Chandler, Apr 07 2009