A132230 Primes congruent to 1 (mod 30).

31, 61, 151, 181, 211, 241, 271, 331, 421, 541, 571, 601, 631, 661, 691, 751, 811, 991, 1021, 1051, 1171, 1201, 1231, 1291, 1321, 1381, 1471, 1531, 1621, 1741, 1801, 1831, 1861, 1951, 2011, 2131, 2161, 2221, 2251, 2281, 2311, 2341, 2371, 2521, 2551, 2671

Offset: 1

Author

Omar E. Pol, Aug 15 2007

Keywords

• nonn
• easy

Comments

Also primes congruent to 1 (mod 15). - N. J. A. Sloane, Jul 11 2008

Primes ending in 1 with (SOD-1)/3 integer where SOD is sum of digits. - Ki Punches, Feb 04 2009

Examples

			From _Muniru A Asiru_, Nov 01 2017: (Start)
31 is a prime and 31 = 30*1 + 1;
61 is a prime and 61 = 30*2 + 1;
151 is a prime and 151 = 30*5 + 1;
211 is a prime and 211 = 30*7 + 1;
241 is a prime and 241 = 30*8 + 1;
271 is a prime and 271 = 30*9 + 1.
(End)
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• C. K. Caldwell, The Prime Pages.
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Cf. A057204, A068228, A129805, A039949, A132231-A132236.

Programs

GAP

A132230 := Filtered(Filtered([1..10^6], n -> n mod 30 = 1), IsPrime); # Muniru A Asiru, Nov 01 2017

Maple

select(isprime, [seq(i,i=1..1000,30)]); # Robert Israel, Jan 19 2016

Mathematica

Select[Range[1, 3000, 30], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2012 *)
Select[Prime[Range[400]],Mod[#,30]==1&] (* Harvey P. Dale, May 21 2021 *)

PARI

is(n)=isprime(n) && n%30==1 \\ Charles R Greathouse IV, Jul 01 2016

Formula

a(n) = A111175(n)*30 + 1. - Ray Chandler, Apr 07 2009

Intersection of A030430 and A002476. - Ray Chandler, Apr 07 2009

Extensions

Edited by Ray Chandler, Apr 07 2009