This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A042978 #53 Aug 16 2024 20:49:27
%S A042978 2,3,17,137,227,977,1187,1493
%N A042978 Stern primes: primes not of the form p + 2b^2 for p prime and b > 0.
%C A042978 No others < 1299709. Are there any others? Related to a conjecture of Goldbach.
%C A042978 The next element of the sequence, if it exists, is larger than 10^9 ; see A060003. - _M. F. Hasler_, Nov 16 2007
%C A042978 The next element, if it exists, is larger than 2*10^13. - _Benjamin Chaffin_, Mar 28 2008
%C A042978 Does not equal A000040(k) + A001105(j) for all k & j >0. - _Robert G. Wilson v_, Sep 07 2012
%D A042978 Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 226.
%D A042978 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 137, p. 46, Ellipses, Paris 2008.
%D A042978 L. E. Dickson, History of the theory of Numbers, vol. 1, page 424.
%H A042978 Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
%H A042978 L. Hodges, <a href="https://www.jstor.org/stable/2690477">A lesser-known Goldbach conjecture</a>, Math. Mag., 66 (1993), 45-47.
%H A042978 Mark VandeWettering, <a href="http://brainwagon.org/?p=2144">Toying with a lesser known Goldbach Conjecture</a>
%H A042978 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%p A042978 N:= 10^6: # to check primes up to N
%p A042978 P:= select(isprime, {2,seq(i,i=3..N,2)}):
%p A042978 S:= {seq(2*b^2,b=1..floor(sqrt(N/2)))}:
%p A042978 P minus {seq(seq(p+s,p=P),s=S)}; # _Robert Israel_, Jan 19 2016
%t A042978 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 *)
%o A042978 (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
%o A042978 (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
%Y A042978 Apart from the first term, a subsequence of A060003.
%K A042978 nonn,more
%O A042978 1,1
%A A042978 _Jud McCranie_