|
| |
|
|
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)
|
|
26
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| 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
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
|
|
|
MATHEMATICA
| t = {1}; sms = {2}; k = 1; Do[k++; While[Intersection[sms, k + t] != {}, k++]; sms = Join[sms, t + k, {2 k}]; AppendTo[t, k], {49}]; t (* T. D. Noe, Mar 02 2011 *)
|
|
|
PROG
| (Haskell)
import Data.Set (Set, empty, insert, member)
a005282 n = a005282_list !! (n-1)
a005282_list = sMianChowla [] 1 empty where
sMianChowla :: [Integer] -> Integer -> Set Integer -> [Integer]
sMianChowla sums z s | s' == empty = sMianChowla sums (z+1) s
| otherwise = z : sMianChowla (z:sums) (z+1) s
where s' = try (z:sums) s
try :: [Integer] -> Set Integer -> Set Integer
try [] s = s
try (x:sums) s | (z+x) `member` s = empty
| otherwise = try sums $ insert (z+x) s
-- Reinhard Zumkeller, Mar 02 2011
|
|
|
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 * A046185 A073336 A134035
Adjacent sequences: A005279 A005280 A005281 * 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
|
| |
|
|
