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A068228 Primes congruent to 1 (mod 12). 55
13, 37, 61, 73, 97, 109, 157, 181, 193, 229, 241, 277, 313, 337, 349, 373, 397, 409, 421, 433, 457, 541, 577, 601, 613, 661, 673, 709, 733, 757, 769, 829, 853, 877, 937, 997, 1009, 1021, 1033, 1069, 1093, 1117, 1129, 1153, 1201, 1213, 1237, 1249, 1297 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, primes of the form x^2+2xy-2y^2 (discriminant 12), cf. A084916. - N. J. A. Sloane, May 31 2014

Also, primes of the form x^2+9y^2 (discriminant 36). - T. D. Noe, May 07 2005

Also, primes of the form x^2+12y^2 (discriminant 48). See A140633. - T. D. Noe, May 19 2008

Is this the same as A141122? - Artur Jasinski, Jun 09 2008

LINKS

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

William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

J. Voight, Quadratic forms that represent almost the same primes, Math. Comp., Vol. 76 (2007), pp. 1589-1617.

MATHEMATICA

Select[Prime/@Range[250], Mod[ #, 12]==1&]

Select[Range[13, 10^4, 12], PrimeQ] (* Zak Seidov, Mar 21 2011 *)

PROG

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

(PARI) forstep(p=13, 10^4, 12, isprime(p)&print(p)); \\ Zak Seidov, Mar 21 2011

(MAGMA) [p: p in PrimesUpTo(1400) | p mod 12 in {1}]; // Vincenzo Librandi, Jul 14 2012

CROSSREFS

Cf. A068227, A068229, A040117, A068231, A068232, A068233, A068234, A068235, A139643, A141122.

Subsequence of A084916.

Also primes in A084916, A020672.

Sequence in context: A238675 A140112 A089030 * A141122 A031339 A034938

Adjacent sequences:  A068225 A068226 A068227 * A068229 A068230 A068231

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

Edited by Dean Hickerson, Feb 27 2002

STATUS

approved

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Last modified July 24 15:24 EDT 2014. Contains 244895 sequences.