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A337190 Numbers k such that A337183(k) and k + A337183(k) are prime.

%I A337190 #20 Feb 06 2021 22:00:06
%S A337190 6,10,22,42,68,102,106,116,126,168,170,178,186,202,230,242,262,356,
%T A337190 366,436,480,502,506,516,610,622,630,638,668,696,716,778,788,798,868,
%U A337190 890,990,1018,1034,1042,1070,1108,1126,1166,1186,1198,1206,1228,1264,1268,1350,1388,1446,1614,1650,1682,1690
%N A337190 Numbers k such that A337183(k) and k + A337183(k) are prime.
%C A337190 All terms are even.
%H A337190 Robert Israel, <a href="/A337190/b337190.txt">Table of n, a(n) for n = 1..10000</a>
%e A337190 a(3) = 22 is a member because A337183(22) = 37 and 37+22 = 59 are both prime.
%p A337190 f:= proc(n) local F, b, i;
%p A337190   F:= sort(map(t -> t[1]$t[2], ifactors(n)[2]), `>`);
%p A337190   b:= convert(F, `+`);
%p A337190   (add(F[i]*b^(i-1), i=1..nops(F)));
%p A337190 end proc:
%p A337190 filter:= proc(n) local v;
%p A337190   v:= f(n); isprime(v) and isprime(v+n)
%p A337190 end proc:
%p A337190 select(filter, 2*[$1..1000]);
%t A337190 Select[Range[2, 1690], AllTrue[If[PrimeQ@ #, #, FromDigits[#, Total[#]] &@ Flatten[ConstantArray @@@ FactorInteger[#]]] + {0, #}, PrimeQ] &] (* _Michael De Vlieger_, Jan 29 2021 *)
%Y A337190 Cf. A337183. Contained in A337185.
%K A337190 nonn,base
%O A337190 1,1
%A A337190 _J. M. Bergot_ and _Robert Israel_, Jan 29 2021