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A201498
a(n) = (prime(n) - 1)*(prime(n+1) - 1)/2 + 3.
1
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).
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Dec 02 2011
STATUS
approved