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 A042978 Stern primes: primes not of the form p + 2b^2 for p prime and b > 0. 5
 2, 3, 17, 137, 227, 977, 1187, 1493 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 Does not equal A000040(k) + A001105(j) for all k & j >0. - Robert G. Wilson v, Sep 07 2012 REFERENCES 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. LINKS L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47. Mark VandeWettering, Toying with a lesser known Goldbach Conjecture MAPLE 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)))}: P minus {seq(seq(p+s, p=P), s=S)}; # Robert Israel, Jan 19 2016 MATHEMATICA 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 *) PROG (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 CROSSREFS Apart from the first term, a subsequence of A060003. Sequence in context: A164816 A259535 A328340 * A089675 A041383 A042903 Adjacent sequences:  A042975 A042976 A042977 * A042979 A042980 A042981 KEYWORD nonn,more AUTHOR STATUS approved

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Last modified October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)