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A generalized difference set on the set of all integers (lambda = 2).
2

%I #17 Oct 13 2015 11:50:54

%S 1,2,6,7,16,18,38,40,82,85,172,175,352,356,714,720,1442,1449,2900,

%T 2907,5816,5824,11650,11658,23318,23327,46656,46666,93334,93345,

%U 186692,186704,373410,373423,746848,746861,1493724,1493738,2987478,2987493,5974988,5975004

%N A generalized difference set on the set of all integers (lambda = 2).

%C In the set of all positive differences of the sequence each integer appears exactly twice, i.e., lambda = 2.

%C 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

%H Danny Rorabaugh, <a href="/A049399/b049399.txt">Table of n, a(n) for n = 0..2500</a>

%H T. Baginova, R. Jajcay, <a href="http://researchgate.net/publication/266348706">Notes on subtractive properties of natural numbers</a>, Bulletin of the ICA, Vol. 25(1999), pp. 29-40

%H O. Grosek, R. Jajcay, <a href="https://zbmath.org/?q=an:0777.05025">Generalized Difference Sets on an Infinite Cyclic Semigroup</a>, JCMCC, Vol. 13 (1993), pp. 167-174.

%F 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

%Y Cf. A024431.

%K nonn,easy

%O 0,2

%A Otokar Grosek (grosek(AT)elf.stuba.sk)

%E a(12)-a(15) corrected and more terms added by _Danny Rorabaugh_, Sep 27 2015