

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


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 A219503 A230387
Adjacent sequences: A060000 A060001 A060002 * A060004 A060005 A060006


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Mar 14 2001


STATUS

approved



