|
| |
|
|
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 1e9. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 16 2007
The next term, if it exists, is larger than 2e13. - Benjamin Chaffin (chaffin(AT)gmail.com), Mar 28 2008
|
|
|
REFERENCES
| David Wells, Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, 1997, page 76.
|
|
|
LINKS
| 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(n-2*s^2), next(2))); print(n)) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 16 2007
|
|
|
CROSSREFS
| Cf. A042978.
Sequence in context: A105630 A199138 A006290 * A025167 A136727 A062873
Adjacent sequences: A060000 A060001 A060002 * A060004 A060005 A060006
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 14 2001
|
| |
|
|
