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Search: id:A060003
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| A060003 |
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Odd numbers not of the form p + 2*k^2, k>0, p prime. |
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+0
7
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OFFSET
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1,2
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COMMENT
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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
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REFERENCES
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David Wells, Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, 1997, page 76.
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LINKS
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Mark VandeWettering, Toying with a lesser known Goldbach Conjecture
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MATHEMATICA
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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 } ]
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PROGRAM
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(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
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CROSSREFS
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Cf. A042978.
Sequence in context: A055214 A105630 A006290 this_sequence A025167 A136727 A120022
Adjacent sequences: A060000 A060001 A060002 this_sequence A060004 A060005 A060006
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 14 2001
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