A320672 a(n) is the smallest divisor of (n+2)*(n+3) not yet in the sequence.

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, 28, 29, 30, 31, 32, 17, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 33, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 44, 56, 57, 58, 59, 60, 61, 62, 63, 64, 55, 66, 67, 68, 69, 70

Offset

0,2

Comments

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

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

Links

Table of n, a(n) for n=0..68.

Example

For n = 0, a(0) = 1 since 1 is the smallest divisor of 6 not yet in the sequence.
For n = 3, a(3) = 3 since 3 is the smallest divisor of 30 not yet in the sequence.

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A002378, A111273, A246368.

Sequence in context: A035506 A246368 A316963 * A367262 A358467 A006016

Adjacent sequences: A320669 A320670 A320671 * A320673 A320674 A320675

Keyword

nonn

Author

Enrique Navarrete, Oct 19 2018

Status

approved