The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A068229 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A068229

Primes congruent to 7 (mod 12).
(history; published version)

#58 by Charles R Greathouse IV at Wed Dec 07 13:02:15 EST 2022

STATUS

editing

approved

#57 by Charles R Greathouse IV at Wed Dec 07 13:02:05 EST 2022

FORMULA

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

PROG

(PARI) is_A068229(n)={n%12==7 && isprime(n)} \\ then, e.g.,

STATUS

approved

editing

#56 by Charles R Greathouse IV at Thu Sep 08 08:45:05 EDT 2022

PROG

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

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#55 by N. J. A. Sloane at Tue Jun 24 01:08:22 EDT 2014

EXTENSIONS

Edited by _Dean Hickerson (dean.hickerson(AT)yahoo.com), _, Feb 27 2002

Discussion

Tue Jun 24

01:08

OEIS Server: https://oeis.org/edit/global/2238

#54 by Michel Marcus at Sun Jun 01 01:38:52 EDT 2014

STATUS

reviewed

approved

#53 by Alonso del Arte at Sat May 31 13:28:40 EDT 2014

STATUS

proposed

reviewed

#52 by Alonso del Arte at Sat May 31 13:28:34 EDT 2014

STATUS

editing

proposed

#51 by Alonso del Arte at Sat May 31 13:28:23 EDT 2014

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.

MATHEMATICA

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

PROG

(PARI) is_A068229(n)={n%12==7 && isprime(n)} \\ then, e.g., select(is_A068229, primes(250)) \\ - _M. F. Hasler_, Jan 25 2013

select(is_A068229, primes(250)) \\ - M. F. Hasler, Jan 25 2013

STATUS

approved

editing

#50 by Alonso del Arte at Sat May 31 13:26:51 EDT 2014

COMMENTS

Primes of the form 3x^2 + 4y^2, with y > 0. - T. D. Noe, May 08 2005

EXAMPLE

31 is in the sequence because 12 * 2 + 7 = 31 and it is prime.

43 = 12 * 3 + 7, and it is prime.

55 is not in the sequence because 12 * 4 + 7 = 5 * 11.

MATHEMATICA

Select[Prime/@Range[250], Mod[ #, 12] == 7 &] (* Adorjan *)

Select[12Range[120] - 5, PrimeQ] (* Alonso del Arte, Dec 28 2013 *)

PROG

(PARI) is_A068229(n)={n%12==7 && isprime(n)} \\ then, e.g., select(is_A068229, primes(250)) \\ - _M. F. Hasler_, Jan 25 2013

select(is_A068229, primes(250)) \\ - M. F. Hasler, Jan 25 2013

CROSSREFS

Cf. A017605 (superset), A068227, A068228, A040117, A068231, A068232, A068233, A068234, A068235, A020677.

KEYWORD

easy,nonn,changed

STATUS

proposed

approved

#49 by Alonso del Arte at Sat May 31 11:18:28 EDT 2014

STATUS

editing

proposed