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 A209321 #12 May 02 2024 04:35:32
%S A209321 4,5,6,7,9,11,14,19,26,38,46,62,70,74,86,94,118,134,194,206,278,286,
%T A209321 566,598,778,842,934,1006,1082,1214,1238,1546,1574,1726,1858,2018,
%U A209321 2278,2474,2774,3142,3686
%N A209321 Indices k for which A209312(k) = 2.
%C A209321 Many of these seem to be even semiprimes.
%C A209321 Is this sequence infinite, and if so, can someone exhibit an explicitly calculable subsequence?
%C A209321 a(42) > 10^5, if it exists. - _Amiram Eldar_, May 02 2024
%t A209321 f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[n_] := pracQ[n] = (ind = Position[(fct = FactorInteger[n])[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most@fct]), _?(# > 1 &)]) == {}; q[n_] := 2 == Sum[If[pracQ[p] && ((PrimeQ[n - p] && PrimeQ[n + p]) || (pracQ[n - p] && pracQ[n + p])), 1, 0], {p, 1, n - 1}]; Select[Range[4000], q] (* _Amiram Eldar_, May 02 2024 *)
%Y A209321 Cf. A209312.
%K A209321 nonn,more
%O A209321 1,1
%A A209321 _M. F. Hasler_, Jan 19 2013
%E A209321 Data corrected by _Amiram Eldar_, May 02 2024