A201498 a(n) = (prime(n) - 1)*(prime(n+1) - 1)/2 + 3.

4, 7, 15, 33, 63, 99, 147, 201, 311, 423, 543, 723, 843, 969, 1199, 1511, 1743, 1983, 2313, 2523, 2811, 3201, 3611, 4227, 4803, 5103, 5409, 5727, 6051, 7059, 8193, 8843, 9387, 10215, 11103, 11703, 12639, 13449, 14279, 15311, 16023, 17103, 18243, 18819, 19407

Offset

1,1

Comments

Consider strictly increasing sequence with the rule:

a(n) is the smallest pairwise sum s of all previous terms such that s > a(n-1).

We start with some pair of coprime positive integers b < c, a(1)=b, a(2)=c; from now on, to find a(n) we use the above-mentioned rule. We observe that, for any seeds b,c, after some term, a(n) = a(n-1) + 1.

E.g., for b=7, c=12, we get 7, 12,1 9, 26, 31, 33, 38, 40, 43, 45, 47, 50, 52, 54, 55, 57, 59, 61, 62, 64, 66, 67, 68, 69, 71, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, ...

We stop at the term a(L=36) = 85 after which a(n) = a(n-1) + 1.

In the general case of arbitrary coprime b < c, the length of the sequence is L = 3 + (b-1)(c-1)/2, and a(L) = b*c + 1.

In A201498, we present the dependence of L(n) for the particular case b=prime(n) and c=prime(n+1).

Links

Table of n, a(n) for n=1..45.

Formula

a(n) = A099407(n) + 3.

Mathematica

#/2+3&/@(Times@@@Partition[Prime[Range[50]]-1, 2, 1])  (* Harvey P. Dale, Jun 01 2015 *)

Prog

(PARI) p=2; forprime(q=3, 1e3, print1((p-1)*(q-1)/2+3", "); p=q) \\ Charles R Greathouse IV, Dec 05 2011

Crossrefs

Sequence in context: A178615 A131935 A119749 * A145970 A232048 A145795

Adjacent sequences: A201495 A201496 A201497 * A201499 A201500 A201501

Keyword

nonn

Author

Zak Seidov, Dec 02 2011

Status

approved