

A127589


Primes of the form 16k+5.


13



5, 37, 53, 101, 149, 181, 197, 229, 277, 293, 373, 389, 421, 613, 661, 677, 709, 757, 773, 821, 853, 997, 1013, 1061, 1093, 1109, 1237, 1301, 1381, 1429, 1493, 1621, 1637, 1669, 1733, 1861, 1877, 1973, 2053, 2069, 2213, 2293, 2309, 2341, 2357, 2389, 2437
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OFFSET

1,1


COMMENTS

All these prime numbers are the sum of two squares. Proof (Artur Jasinski): according to Fermat's theorem all prime numbers of the form 4n+1 are sum of two squares, and 16k+5 = 4(4k+1)+1 are of this form.


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000


MATHEMATICA

a = {}; Do[If[PrimeQ[16n + 5], AppendTo[a, 16n + 5]], {n, 0, 200}]; a


CROSSREFS

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587.
Sequence in context: A173826 A071680 A141182 * A244374 A238477 A213049
Adjacent sequences: A127586 A127587 A127588 * A127590 A127591 A127592


KEYWORD

nonn


AUTHOR

Artur Jasinski, Jan 19 2007


EXTENSIONS

Invalid comment removed  Zak Seidov, Jul 22 2010


STATUS

approved



