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A337028 Numbers k such that k + A001414(k), k - A001414(k) and k mod A001414(k) are all prime.

%I A337028 #10 Feb 06 2021 21:59:18
%S A337028 10,12,14,15,20,26,33,35,38,51,65,68,86,96,111,112,116,161,201,203,
%T A337028 206,209,215,221,278,297,300,304,321,371,395,398,413,420,471,533,545,
%U A337028 551,570,626,671,698,720,755,779,803,837,858,866,910,972,1020,1046,1124,1155,1161,1286,1326,1349,1385
%N A337028 Numbers k such that k + A001414(k), k - A001414(k) and k mod A001414(k) are all prime.
%H A337028 Robert Israel, <a href="/A337028/b337028.txt">Table of n, a(n) for n = 1..10000</a>
%e A337028 a(3)=14 is in the sequence because A001414(14)=9, and 14-9=5, 14+9=23 and 14 mod 9 = 5 are all prime.
%p A337028 A001414:= proc(n) local F; F:= ifactors(n)[2]; convert(map(convert,F,`*`),`+`) end proc:
%p A337028 filter:= proc(n) local s; s:= A001414(n); isprime(n+s) and isprime(n-s) and isprime(n mod s) end proc:
%p A337028 select(filter, [$1..2000]);
%Y A337028 Cf. A001414. Subset of A050705.
%K A337028 nonn
%O A337028 1,1
%A A337028 _J. M. Bergot_ and _Robert Israel_, Aug 11 2020