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 A141340 #11 Jan 22 2025 11:56:13
%S A141340 1,2,3,4,5,6,7,8,10,12,14,16,18,24,30,36,42,48,60,90,210
%N A141340 Positive integers n such that A061358(n) = #{primes p | n/2 <= p < n-1}.
%C A141340 According to Brouwers et al., Deshouillers et al. showed that the maximum term of this sequence is 210. A141341 is a subsequence.
%C A141340 Positive integers k such that, for each prime p with k/2 <= p <= k - 2, k - p is prime. - _Charles R Greathouse IV_, May 28 2017
%H A141340 J-M. Deshouillers, A. Granville, W. Narkiewicz and C. Pomerance, <a href="https://doi.org/10.1090/S0025-5718-1993-1202609-9">An upper bound in Goldbach's problem</a>, Math. Comp. 61 (1993), 209-213.
%H A141340 Brady Haran and Carl Pomerance, <a href="https://www.youtube.com/watch?v=PEMIxDjSRTQ">210 is VERY Goldbachy</a>, Numberphile video (2017)
%H A141340 David van Golstein Brouwers, John Bamberg and Grant Cairns, <a href="http://www.austms.org.au/Publ/Gazette/2004/Sep04/brouwers.pdf">Totally Goldbach numbers and related conjectures</a>, The Australian Mathematical Society, Gazette, Volume 31 Number 4, September 2004.
%e A141340 For each prime 210/2 <= p <= 210, 210 - p is prime, and so 210 is in this sequence: 210 - 107 = 103, 210 - 109 = 101, 210 - 113 = 97, 210 - 127 = 83, 210 - 131 = 79, 210 - 137 = 73, 210 - 139 = 71, 210 - 149 = 61, 210 - 151 = 59, 210 - 157 = 53, 210 - 163 = 47, 210 - 167 = 43, 210 - 173 = 37, 210 - 179 = 31, 210 - 181 = 29, 210 - 191 = 19, 210 - 193 = 17, 210 - 197 = 13, 210 - 199 = 11. - _Charles R Greathouse IV_, May 28 2017
%t A141340 Block[{r = {}}, Do[ If[ AllTrue[i - #, PrimeQ] &@ NextPrime[i/2, Range[ PrimePi[i - 2] - PrimePi[i/2]]], AppendTo[r, i]], {i, 210}]; r] (* _Mikk Heidemaa_, May 29 2024 *)
%o A141340 (PARI) is(n)=forprime(p=n/2,n-2, if(!isprime(n-p),return(0))); 1 \\ _Charles R Greathouse IV_, May 28 2017; corrected by _Michel Marcus_, May 30 2024
%Y A141340 Cf. A061358, A141341.
%K A141340 nonn,nice,fini,full
%O A141340 1,2
%A A141340 _Rick L. Shepherd_, Jun 25 2008