A320672 - OEIS

%I #41 Dec 20 2018 23:46:33

%S 1,2,4,3,6,7,8,5,10,11,12,13,14,15,16,9,18,19,20,21,22,23,24,25,26,27,

%T 28,29,30,31,32,17,34,35,36,37,38,39,40,41,42,43,33,45,46,47,48,49,50,

%U 51,52,53,54,44,56,57,58,59,60,61,62,63,64,55,66,67,68,69,70

%N a(n) is the smallest divisor of (n+2)*(n+3) not yet in the sequence.

%C a(n) is the smallest divisor of A002378(n+2) not yet in the sequence.

%C The numbers that are smaller than the preceding terms are: 3, 5, 9, 17, 33, 44, 55, 65, 90, 99, 143, 208, ...

%e For n = 0, a(0) = 1 since 1 is the smallest divisor of 6 not yet in the sequence.

%e For n = 3, a(3) = 3 since 3 is the smallest divisor of 30 not yet in the sequence.

%t s = {}; Do[d = Divisors[(n + 2)(n + 3)]; Do[d1 = d[[k]]; If[FreeQ[s, d1], AppendTo[s, d1]; Break[]], {k, Length[d]}], {n, 0, 100}]; s (* _Amiram Eldar_, Nov 14 2018 *)

%o (PARI) toadd(n, v) = {fordiv(n, d, if (!vecsearch(v, d), return(d)); ); }

%o lista(nn) = {v = []; for (n = 0, nn, newt = toadd((n+2)*(n+3), v); print1(newt, ", "); v = vecsort(concat(v, newt)); ); } \\ _Michel Marcus_, Nov 20 2018

%Y Cf. A002378, A111273, A246368.

%K nonn

%O 0,2

%A _Enrique Navarrete_, Oct 19 2018