A042978 Stern primes: primes not of the form p + 2b^2 for p prime and b > 0.

2, 3, 17, 137, 227, 977, 1187, 1493

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

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

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.

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

L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.

Mark VandeWettering, Toying with a lesser known Goldbach Conjecture

Index entries for sequences related to 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: A135726 A259535 A328340 * A089675 A041383 A042903

Adjacent sequences: A042975 A042976 A042977 * A042979 A042980 A042981

Keyword

nonn,more

Author

Jud McCranie

Status

approved