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Numbers k such that k + A001414(k), k - A001414(k) and k mod A001414(k) are all prime.
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%I #10 Feb 06 2021 21:59:18

%S 10,12,14,15,20,26,33,35,38,51,65,68,86,96,111,112,116,161,201,203,

%T 206,209,215,221,278,297,300,304,321,371,395,398,413,420,471,533,545,

%U 551,570,626,671,698,720,755,779,803,837,858,866,910,972,1020,1046,1124,1155,1161,1286,1326,1349,1385

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

%H Robert Israel, <a href="/A337028/b337028.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 A001414:= proc(n) local F; F:= ifactors(n)[2]; convert(map(convert,F,`*`),`+`) end proc:

%p filter:= proc(n) local s; s:= A001414(n); isprime(n+s) and isprime(n-s) and isprime(n mod s) end proc:

%p select(filter, [$1..2000]);

%Y Cf. A001414. Subset of A050705.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Aug 11 2020