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Numbers k such that (prime(k) mod 5) == 2 (mod 3).
4

%I #20 Feb 04 2024 11:33:03

%S 1,4,7,12,15,19,25,28,31,33,37,39,45,49,55,59,63,66,68,69,73,78,88,91,

%T 93,101,102,106,107,111,113,118,123,129,134,138,139,144,148,151,154,

%U 155,159,161,163,165,168,181,184,187,195,199,203,206,211,214,217

%N Numbers k such that (prime(k) mod 5) == 2 (mod 3).

%C Every positive integer is in exactly one of the sequences A244739, A024707, A244741.

%H Clark Kimberling, <a href="/A244741/b244741.txt">Table of n, a(n) for n = 1..1000</a>

%e n ... prime(n) mod 5 mod 3

%e 1 ..... 2 ..... 2 ... 2

%e 2 ..... 3 ..... 3 ... 0

%e 3 ..... 5 ..... 0 ... 0

%e 4 ..... 7 ..... 2 ... 2

%e 5 ..... 11 .... 1 ... 1

%e 6 ..... 13 .... 3 ... 0

%p A244741:=n->`if`(((ithprime(n) mod 5) mod 3) = 2, n, NULL): seq(A244741(n), n=1..250); # _Wesley Ivan Hurt_, Jul 06 2014

%t z = 300; u = Mod[Table[Mod[Prime[n], 5], {n, 1, z}], 3] (* A244738 *)

%t v1 = Flatten[Position[u, 0]] (* A244739 *)

%t v2 = Flatten[Position[u, 1]] (* A024707 *)

%t v3 = Flatten[Position[u, 2]] (* A244741 *)

%Y Cf. A039703, A244738, A244739, A024707, A244735. Essentially the same as A049509.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jul 05 2014