



7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 911, 919, 967, 983, 991, 1031, 1039, 1063, 1087, 1103, 1151, 1223, 1231
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OFFSET

1,1


COMMENTS

Original title was "Primes of the form x^2 + 4xy + 4y^2 (as well as of the form 7x^2 + 12xy + 4y^2)."
R. J. Mathar was the first to wonder if this entry is a duplicate. By elementary means, I very easily proved that all primes of this form are also of the form 8n + 7 (which is A007522). Then Don Reble demonstrated that each prime of the form 8n + 7 has a corresponding representation as x^2 + 4xy + 4y^2. Therefore the two sequences are in fact the same.  Alonso del Arte, Nov 21 2016


LINKS

Table of n, a(n) for n=1..51.


CROSSREFS

Sequence in context: A263874 A014663 A007522 * A295196 A287309 A275777
Adjacent sequences: A141172 A141173 A141174 * A141176 A141177 A141178


KEYWORD

nonn,dead


AUTHOR

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 12 2008


EXTENSIONS

More terms from Colin Barker, Apr 05 2015


STATUS

approved



