A132231 Primes congruent to 7 (mod 30).

7, 37, 67, 97, 127, 157, 277, 307, 337, 367, 397, 457, 487, 547, 577, 607, 727, 757, 787, 877, 907, 937, 967, 997, 1087, 1117, 1237, 1297, 1327, 1447, 1567, 1597, 1627, 1657, 1747, 1777, 1867, 1987, 2017, 2137, 2287, 2347, 2377, 2437, 2467, 2557, 2617, 2647

Offset

1,1

Comments

Primes ending in 7 with (SOD-1)/3 integer where SOD is sum of digits. - Ki Punches, Feb 07 2009

Intersection of A030432 and A002476. - Ray Chandler, Apr 07 2009

Only from 4927 on, there are more composite numbers than primes in {7+30k}, see A227869. - M. F. Hasler, Nov 02 2013

Terms are non-twin primes A007510, except for 7. - Jonathan Sondow, Oct 27 2017

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

C. K. Caldwell, The Prime Pages

Omar E. Pol, Prime numbers in a sieve with 30 columns

Omar E. Pol, Sobre el patrón de los números primos

Formula

a(n) = A158573(n)*30 + 7. - Ray Chandler, Apr 07 2009

a(n) = A211890(4,n-1) for n <= 5. - Reinhard Zumkeller, Jul 13 2012

Mathematica

Select[30*Range[0, 100]+7, PrimeQ] (* Harvey P. Dale, Feb 01 2012 *)
Select[Prime[Range[1000]], MemberQ[{7}, Mod[#, 30]]&] (* Vincenzo Librandi, Aug 14 2012 *)

Prog

(Haskell)
a132231 n = a132231_list !! (n-1)
a132231_list = [x | k <- [0..], let x = 30 * k + 7, a010051' x == 1]
-- Reinhard Zumkeller, Jul 13 2012
(Magma) [p: p in PrimesUpTo(3000) | p mod 30 eq 7 ]; // Vincenzo Librandi, Aug 14 2012
(PARI) forstep(p=7, 1999, 30, isprime(p)&&print1(p", ")) \\ M. F. Hasler, Nov 02 2013

Crossrefs

Cf. A007510, A007528, A010051, A068229, A117047, A129807, A039949, A132230-A132236, A214360.

Sequence in context: A123085 A128471 A168003 * A289353 A221982 A104915

Adjacent sequences: A132228 A132229 A132230 * A132232 A132233 A132234

Keyword

nonn,easy

Author

Omar E. Pol, Aug 15 2007

Extensions

Extended by Ray Chandler, Apr 07 2009

Status

approved