1,1

No others < 1299709. Are there any others?

Related to a conjecture of Goldbach.

The next term of the sequence, if it exists, is larger than 10^9; see A060003. - M. F. Hasler, Nov 16 2007

The next term, if it exists, is larger than 2*10^13. - Benjamin Chaffin, Mar 28 2008

Does not equal A000040(k) + A001105(j) for all k and j > 0. - Robert G. Wilson v, Sep 07 2012

Named after the German mathematician Moritz Abraham Stern (1807-1894). - Amiram Eldar, Feb 01 2026

Albert H. Beiler, Recreations in the theory of numbers, Dover, New York, 2nd ed., 1966. See p. 226.

Jean-Marie 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, Chelsea, N.Y., 1952, page 424.

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph.D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Laurent Hodges, A lesser-known Goldbach conjecture, Math. Mag., Vol. 66, No. 1 (1993), 45-47.

Moritz A. Stern, Sur un assertion de Goldbach relative aux nombres impairs, Nouvelles Annales Math., Vol. 15 (1856), pp. 23-24.

Mark VandeWettering, Toying with a lesser known Goldbach Conjecture.

Wikipedia, Stern prime.

Index entries for sequences related to Goldbach conjecture.

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

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 *)

(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

Apart from the first term, a subsequence of A060003.

Cf. A000040, A001105.

Sequence in context: A135726 A259535 A328340 * A089675 A388062 A041383

Adjacent sequences: A042975 A042976 A042977 * A042979 A042980 A042981

nonn,more

approved