OFFSET
1,2
COMMENTS
Except for 1 & 4, all the rest of the terms are prime. They have a density of about 4/5 of the primes for the first 2500 terms. Primes not a member of this sequence: 3, 5, 11, 17, 23, 31, 41, 47, 61, 71, 83, 101, 107, 113, 131, 139, 151, 167, 181, 193, 199, ..., . - Robert G. Wilson v, Aug 31 2009
Conjecture: No two consecutive primes are absent from this sequence (other than 3 and 5). (Equivalently, if p < q < r are consecutive primes and q > 5 is not a term, then p and r are terms.) See A164980. - Rick L. Shepherd, Sep 03 2009
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..3500
EXAMPLE
The first 4 terms are 1,2,4,7. The sums of every pair of distinct terms are: 1+2=3, 1+4=5, 2+4=6, 7+1=8, 7+2=9, and 7+4=11. So we are looking for the smallest integer > 7 that is coprime to 3, 5, 6, 8, 9, and 11. This number, which is a(5), is 13.
MATHEMATICA
a[1] = 1; a[2] = 2; a[n_] := a[n] = Block[{k = a[n - 1] + 1, t = Plus @@@ Subsets[Array[a, n - 1], {2}]}, While[ Union@ GCD[t, k] != {1}, k++ ]; k]; Array[a, 59] (* Robert G. Wilson v, Aug 31 2009 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 30 2009
EXTENSIONS
a(12) and onward from Robert G. Wilson v, Aug 31 2009
STATUS
approved