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 A141341 #13 Jul 22 2025 10:34:11
%S A141341 1,2,3,4,5,6,8,10,12,18,24,30
%N A141341 Totally Goldbach numbers: Positive integers k such that for all primes p < k-1 with p not dividing k, k-p is prime.
%C A141341 As Browers et al. point out, A141340 = A141341 union {7,14,16,36,42,48,60,90,210}, A020490 = A141341\{5} and A048597 = A141341\{5,10}. The authors show that the first strategy of Deshouillers et al. to establish a bound (of 10^520) for A141340 is sufficient for then determining the totally Goldbach numbers and "leads us naturally to interesting questions concerning primes in a fixed residue class".
%H A141341 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 A141341 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.
%H A141341 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%t A141341 q[k_]:=AllTrue[k-Select[Prime[Range[PrimePi[k-2]]],!Divisible[k,#]&],PrimeQ];Select[Range[30],q[#]&] (* _James C. McMahon_, Jul 21 2025 *)
%Y A141341 Cf. A020490, A048597, A141340.
%K A141341 fini,full,nonn
%O A141341 1,2
%A A141341 _Rick L. Shepherd_, Jun 25 2008