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 A303403 #23 Nov 25 2024 05:00:12
%S A303403 2,4,12,18,24,26,30,32,38,40,50,54,56,60,66,68,74,80,92,96,102,104,
%T A303403 106,110,116,122,128,136,146,148,152,154,156,164,170,172,178,180,200,
%U A303403 204,206,212,226,230,234,248,256,260,264,268,276,290,292,296,298,302
%N A303403 Even numbers that are not the sum of two prime-indexed primes.
%C A303403 Bayless et al. conjectured that every even number larger than 80612 is the sum of two prime-indexed primes. If the conjecture is true then this sequence is finite with 733 terms.
%C A303403 Similarly, it appears that 322704332 is the largest of the 1578727 even numbers that cannot be written as prime(prime(prime(i))) + prime(prime(prime(j))). - _Giovanni Resta_, May 31 2018
%H A303403 Jonathan Bayless, Dominic Klyve, and Tomás Oliveira e Silva, <a href="http://www.emis.de/journals/INTEGERS/papers/n43/n43.Abstract.html">New Bounds and Computations on Prime-Indexed Primes</a>, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A43, 2013.
%e A303403 20 is not in the sequence since 20 = 17 + 3 = prime(7) + prime(2). 2 and 7 are primes, so 3 and 17 are prime-indexed primes. - _Michael B. Porter_, May 21 2018
%t A303403 pipQ[n_]:=PrimeQ[n]&&PrimeQ[PrimePi[n]]; s1falsifiziertQ[s_]:= Module[{ip=IntegerPartitions[s, {2}], widerlegt=False}, Do[If[pipQ[ip[[i, 1]] ] ~And~ pipQ [ip[[i, 2]] ], widerlegt = True; Break[]], {i, 1, Length[ip]}]; widerlegt]; Select[Range[2500],EvenQ[#]&& s1falsifiziertQ[ # ]==False&] (* after _Michael Taktikos_ at A014092 *)
%t A303403 (* or *) p = Prime@ Prime@ Range@ PrimePi@ PrimePi@ 302; Select[Range[2, 302, 2], IntegerPartitions[#, {2}, p] == {} &] (* _Giovanni Resta_, May 31 2018 *)
%o A303403 (PARI) isok(n) = {if (n % 2, return (0)); forprime(p=2, n/2, if (isprime(primepi(p)) && isprime(n-p) && isprime(primepi(n-p)), return (0));); return (1);} \\ _Michel Marcus_, May 18 2018
%Y A303403 Cf. A006450, A014092, A166081.
%Y A303403 Equals 2*A174682. - _Michel Marcus_, May 18 2018
%K A303403 nonn
%O A303403 1,1
%A A303403 _Amiram Eldar_, May 13 2018