

A060003


Odd numbers not of the form p + 2*k^2, k>0, p prime.


6




OFFSET

1,2


COMMENTS

This sequence is probably finite.
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 10^9.  M. F. Hasler, Nov 16 2007
The next term, if it exists, is larger than 2 * 10^13.  Benjamin Chaffin, Mar 28 2008
Terms greater than 3 are of the form 6n1.  Dan Graham, Mar 03 2015


REFERENCES

David Wells, Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, 1997, page 76.


LINKS

Table of n, a(n) for n=1..10.
Laurent Hodges, A lesserknown Goldbach conjecture, Math. Mag., 66 (1993), 4547.
Mark VandeWettering, Toying with a lesser known Goldbach Conjecture


MATHEMATICA

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 } ]


PROG

(PARI) forstep( n=1, 2^30, 2, for(s=1, sqrtint(n\2), if(isprime(n2*s^2), next(2))); print(n)) \\ M. F. Hasler, Nov 16 2007


CROSSREFS

Cf. A042978.
Sequence in context: A105630 A199138 A006290 * A231909 A244432 A219503
Adjacent sequences: A060000 A060001 A060002 * A060004 A060005 A060006


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Mar 14 2001


STATUS

approved



