OFFSET
0,2
COMMENTS
In the set of all positive differences of the sequence each integer appears exactly twice, i.e., lambda = 2.
One could try to greedily build such a difference set as follows: b(1) = 1, b(n+1) = b(n)+j with j the smallest difference yet to appear twice. This would begin with {1, 2, 3, 5, 8, 12, 17, 23, 31, 39, 49} and fail; the smallest difference yet to appear twice is then 12 = 17-5, but 49+12 = 61 and 61-39 = 22 = 23-1 = 39-17. - Danny Rorabaugh, Sep 27 2015
LINKS
Danny Rorabaugh, Table of n, a(n) for n = 0..2500
T. Baginova, R. Jajcay, Notes on subtractive properties of natural numbers, Bulletin of the ICA, Vol. 25(1999), pp. 29-40
O. Grosek, R. Jajcay, Generalized Difference Sets on an Infinite Cyclic Semigroup, JCMCC, Vol. 13 (1993), pp. 167-174.
FORMULA
Let N_1={1, 2}. Given N_i, let N_{i+1} = N_i union {2k+2, 2k+2+j} where k = max element of N_i and j = smallest number of form x-y for at most one pair x, y in N_i, x>y. Union of all N_i gives sequence. - Danny Rorabaugh (mirroring formula in A024431), Sep 27 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Otokar Grosek (grosek(AT)elf.stuba.sk)
EXTENSIONS
a(12)-a(15) corrected and more terms added by Danny Rorabaugh, Sep 27 2015
STATUS
approved