|
Search: id:A005282
|
|
|
| A005282 |
|
Mian-Chowla sequence (a B_2 sequence): a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the pairwise sums of elements are all distinct.
(Formerly M1094)
|
|
+0
25
|
|
| 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182, 204, 252, 290, 361, 401, 475, 565, 593, 662, 775, 822, 916, 970, 1016, 1159, 1312, 1395, 1523, 1572, 1821, 1896, 2029, 2254, 2379, 2510, 2780, 2925, 3155, 3354, 3591, 3797, 3998, 4297, 4433, 4779, 4851
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
An alternative definition is to start with 1 and then continue with the least number such that all pairwise differences of distinct elements are all distinct. - Jens Voss, Feb 04, 2003
R. Lewis points out, at the first Weisstein link, that S, the sum of the reciprocals of this sequence, satisfies 2.158435 =< S =< 2.158677. Similarly, the sum of the squares of reciprocals of this sequence converges to approximately 1.33853369 and the sum of the cube of reciprocals of this sequence converges to approximately 1.14319352. - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 21 2004
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.20.2.
R. K. Guy, Unsolved Problems in Number Theory, E28.
A. M. Mian and S. D. Chowla, On the B_2-sequences of Sidon, Proc. Nat. Acad. Sci. India, A14 (1944), 3-4.
Zhang Zhen-Xiang, A B_2-sequence with larger reciprocal sum, Math. Comp. 60 (1993), 835-839.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..5818 (terms less than 2*10^9)
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for B_2 sequences.
|
|
EXAMPLE
|
The second term is 2 because the 3 pairwise sums 1+1=2, 1+2=3, 2+2=4 are all distinct.
The third term cannot be 3 because 1+3 = 2+2. But it can be 4, since 1+4=5, 2+4=6, 4+4=8 are distinct and distinct from the earler sums 1+1=2, 1+2=3, 2+2=4.
|
|
CROSSREFS
|
a(n) = A025582(n)+1. Cf. A051788, A080200 (for differences between terms).
Different from A046185. Cf. A011185.
Equals (A034757(n)+1)/2.
Sequence in context: A115266 A026039 A004978 this_sequence A046185 A073336 A134035
Adjacent sequences: A005279 A005280 A005281 this_sequence A005283 A005284 A005285
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com) and Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
EXTENSIONS
|
Examples added by N. J. A. Sloane (njas(AT)research.att.com), Jun 01 2008
|
|
|
Search completed in 0.002 seconds
|
