A068229 Primes congruent to 7 (mod 12).

7, 19, 31, 43, 67, 79, 103, 127, 139, 151, 163, 199, 211, 223, 271, 283, 307, 331, 367, 379, 439, 463, 487, 499, 523, 547, 571, 607, 619, 631, 643, 691, 727, 739, 751, 787, 811, 823, 859, 883, 907, 919, 967, 991, 1039, 1051, 1063, 1087, 1123, 1171, 1231

Offset: 1

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Feb 22 2002

Keywords

• easy
• nonn

Comments

Primes of the form 3x^2 + 4y^2. - T. D. Noe, May 08 2005

It appears that all terms starting from term 103 are primes which are the sum of 5 positive (n > 0) different squares in more than one way (A193143) - Vladimir Joseph Stephan Orlovsky, Jul 16 2011.

Links

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

Crossrefs

Cf. A068227, A068228, A040117, A068231, A068232, A068233, A068234, A068235.

Programs

Magma

[ p: p in PrimesUpTo(1400) | p mod 12 in {7} ]; // Vincenzo Librandi, Jul 14 2012

Mathematica

Select[Prime/@Range[250], Mod[#, 12] == 7 &]

PARI

for(i=1,250, if(prime(i)%12==7, print(prime(i))))

PARI

is_A068229(n)=n%12==7 && isprime(n) \\ then, e.g.,
select(is_A068229, primes(250))  \\ - M. F. Hasler, Jan 25 2013

Formula

a(n) ~ 4n log n. - Charles R Greathouse IV, Dec 07 2022

Extensions

Edited by Dean Hickerson, Feb 27 2002