%I A060003
%S A060003 1,3,17,137,227,977,1187,1493,5777,5993
%N A060003 Odd numbers not of the form p + 2*k^2, k>0, p prime.
%C A060003 This sequence is probably finite.
%C A060003 Goldbach conjectured that all odd composites are sum of a prime and twice 
               a square. a[9]=5777 and a[10]=5993 are the only known exceptions. 
               Elements a[2]..a[8] are the odd Stern primes (cf. A042978). The next 
               element of the sequence, if it exists, is larger than 1e9. - M. F. 
               Hasler (Maximilian.Hasler(AT)gmail.com), Nov 16 2007
%C A060003 The next term, if it exists, is larger than 2e13. - Benjamin Chaffin 
               (chaffin(AT)gmail.com), Mar 28 2008
%D A060003 David Wells, Penguin Dictionary of Curious and Interesting Numbers, Revised 
               Edition, Penguin Books, London, 1997, page 76.
%H A060003 Mark VandeWettering, <a href="http://brainwagon.org/?p=2144">Toying with 
               a lesser known Goldbach Conjecture</a>
%t A060003 Do[ k = 1; While[ n - 2*k^2 > 1 && !PrimeQ[ n - 2*k^2 ], k++ ]; If[ n 
               - 2*k^2 < 0, Print[n] ], { n, 5, 10^8 } ]
%o A060003 (PARI) forstep( n=1,2^30,2, for(s=1,sqrtint(n\2), if(isprime(n-2*s^2),
               next(2)));print(n)) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Nov 16 2007
%Y A060003 Cf. A042978.
%Y A060003 Sequence in context: A055214 A105630 A006290 this_sequence A025167 A136727 
               A120022
%Y A060003 Adjacent sequences: A060000 A060001 A060002 this_sequence A060004 A060005 
               A060006
%K A060003 nonn
%O A060003 1,2
%A A060003 Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 14 2001