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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
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.
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
KEYWORD
nonn,more
AUTHOR
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)