

A049399


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


2



1, 2, 6, 7, 16, 18, 38, 40, 82, 85, 172, 175, 352, 356, 714, 720, 1442, 1449, 2900, 2907, 5816, 5824, 11650, 11658, 23318, 23327, 46656, 46666, 93334, 93345, 186692, 186704, 373410, 373423, 746848, 746861, 1493724, 1493738, 2987478, 2987493, 5974988, 5975004
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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 = 175, but 49+12 = 61 and 6139 = 22 = 231 = 3917.  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. 2940
O. Grosek, R. Jajcay, Generalized Difference Sets on an Infinite Cyclic Semigroup, JCMCC, Vol. 13 (1993), pp. 167174.


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 xy 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

Cf. A024431.
Sequence in context: A286054 A030607 A177353 * A060133 A107784 A210619
Adjacent sequences: A049396 A049397 A049398 * A049400 A049401 A049402


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



