[seqfan] A127589 Primes of the form 16k+5: prime k(?)
zak seidov
zakseidov at yahoo.com
Thu Jul 22 07:24:55 CEST 2010
Values of k in A127589 are not always a sum of two squares (see A127590),
and %C A127589 may be shortened to:
%C A127589 All these prime numbers are the sum of two squares.
Or even better,
%C A127589 may be totally omitted (?)
Zak
%%%%%%%%%%% as at present in OEIS %%%%%%%%%%%%%%%%%%%%%
%S A127589 5,37,53,101,149,181,197,229,277,293,373,389,421,613,661,677,709,757,
%N A127589 Primes of the form 16k+5.
%C A127589 All these prime numbers are the sum of two squares and k is also a sum
of two squares. Proof (Artur Jasinski): according to Fermat's theorem
all prime numbers of the form 4n+1 are sum of two squres. Also 16k+5
= 4(4k+1)+1.
%S A127590 0,2,3,6,9,11,12,14,17,18,23,24,26,38,41,42,44,47,48,51,53,62,63,66,68,
%N A127590 Numbers n such that 16n+5 is prime.
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