

A042978


Stern primes: primes not of the form p + 2b^2 for p prime and b > 0.


5




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

Table of n, a(n) for n=1..8.
L. Hodges, A lesserknown Goldbach conjecture, Math. Mag., 66 (1993), 4547.
Mark VandeWettering, Toying with a lesser known Goldbach Conjecture
Index entries for sequences related to Goldbach conjecture


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(n2*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(p2*k^2), next(2))); print1(p", ")) \\ Charles R Greathouse IV, Aug 04 2011


CROSSREFS

Subsequence of A060003.
Sequence in context: A135726 A164816 A259535 * A089675 A041383 A042903
Adjacent sequences: A042975 A042976 A042977 * A042979 A042980 A042981


KEYWORD

nonn,more


AUTHOR

Jud McCranie


STATUS

approved



