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A042978
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Stern primes: primes not of the form p + 2b^2 for p prime and b > 0.
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5
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OFFSET
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1,1
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COMMENTS
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No others < 1299709. Are there any others? Related to a conjecture of Goldbach.
The next element of the sequence, if it exists, is larger than 10^9 ; see A060003. - M. F. Hasler, Nov 16 2007
The next element, if it exists, is larger than 2*10^13. - Benjamin Chaffin, Mar 28 2008
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 137, p. 46, Ellipses, Paris 2008.
L. E. Dickson, History of the theory of Numbers, vol. 1, page 424.
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LINKS
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MAPLE
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N:= 10^6: # to check primes up to N
P:= select(isprime, {2, seq(i, i=3..N, 2)}):
S:= {seq(2*b^2, b=1..floor(sqrt(N/2)))}:
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MATHEMATICA
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fQ[n_] := Block[{k = Floor[ Sqrt[ n/2]]}, While[k > 0 && !PrimeQ[n - 2*k^2], k--]; k == 0]; Select[ Prime[Range[238]], fQ] (* Robert G. Wilson v, Sep 07 2012 *)
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PROG
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(PARI) forprime( n=1, default(primelimit), for(s=1, sqrtint(n\2), if(isprime(n-2*s^2), next(2))); print(n)) \\ M. F. Hasler, Nov 16 2007
(PARI) forprime(p=2, 4e9, forstep(k=sqrt(p\2), 1, -1, if(isprime(p-2*k^2), next(2))); print1(p", ")) \\ Charles R Greathouse IV, Aug 04 2011
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CROSSREFS
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Apart from the first term, a subsequence of A060003.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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