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

10, 12, 14, 15, 20, 26, 33, 35, 38, 51, 65, 68, 86, 96, 111, 112, 116, 161, 201, 203, 206, 209, 215, 221, 278, 297, 300, 304, 321, 371, 395, 398, 413, 420, 471, 533, 545, 551, 570, 626, 671, 698, 720, 755, 779, 803, 837, 858, 866, 910, 972, 1020, 1046, 1124, 1155, 1161, 1286, 1326, 1349, 1385

Offset: 1

Author

J. M. Bergot and Robert Israel, Aug 11 2020

Keywords

• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414. Subset of A050705.

Programs

Maple

A001414:= proc(n) local F; F:= ifactors(n)[2]; convert(map(convert,F,`*`),`+`) end proc:
filter:= proc(n) local s; s:= A001414(n); isprime(n+s) and isprime(n-s) and isprime(n mod s) end proc:
select(filter, [$1..2000]);