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A036241
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a(1)=1, a(2)=2, a(3)=3; for n >= 3, a(n) is smallest number such that all a(i) for 1 <= i <= n are distinct, all a(i)+a(j) for 1 <= i < j <= n are distinct and all a(i)+a(j)+a(k) for 1 <= i < j < k <= n are distinct.
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4
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1, 2, 3, 5, 8, 14, 25, 45, 82, 140, 235, 388, 559, 839, 1286, 1582, 2221, 3144, 4071, 5795, 6872, 9204, 11524, 13796, 17686, 21489, 26019, 31080, 37742, 45067, 53144, 58365, 67917, 78484, 91767, 106513, 118600, 133486, 147633, 166034, 174717
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Letter from V. Jooste, Pretoria, South Africa, Sep. 8, 1975.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..75
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EXAMPLE
| For {1,2,3,4} we have 1+4 = 2+3, so a(4) is not 4. For {1,2,3,5} the terms 1, 2, 3, 5 are distinct, the sums 1+2, 1+3, 1+5, 2+3, 2+5, 3+5 are distinct and the sums 1+2+3, 1+2+5, 1+3+5, 2+3+5 are distinct, so a(4) = 5.
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PROG
| (PARI) {unique(v)=local(b); b=1; for(j=2, length(v), if(v[j-1]==v[j], b=0)); b}
{newsort(u, v, q)=local(s); s=[]; for(i=1, length(v), s=concat(s, v[i]+q)); vecsort(concat(u, s))}
{m=175000; print1(1, ", ", 2, ", ", 3, ", "); w1=[1, 2, 3]; w2=[3, 4, 5]; w3=[6]; q=4; while(q<m, y1=concat(w1, q); y2=newsort(w2, w1, q); y3=newsort(w3, w2, q); if(unique(y1)&&unique(y2)&&unique(y3), w1=y1; w2=y2; w3=y3; print1(q, ", ")); q=q+1)}
(Haskell)
import qualified Data.Set as Set (null, map)
import Data.Set (empty, fromList, toList, intersect, union)
a036241 n = a036241_list !! (n-1)
a036241_list = f [1..] [] empty empty where
f (x:xs) ys s2 s3
| null (s2' `intersect` y2s) && null (s3' `intersect` y3s)
= x : f xs (x:ys) (fromList s2' `union` s2) (fromList s3' `union` s3)
| otherwise = f xs ys s2 s3
where s2' = sort $ map (x +) ys
s3' = sort $ map (x +) y2s
y2s = toList s2
y3s = toList s3
-- Reinhard Zumkeller, Oct 02 2011
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CROSSREFS
| Cf. A062065, A051912, A060276.
Sequence in context: A091956 A107480 A128021 * A192633 A125028 A119262
Adjacent sequences: A036238 A036239 A036240 * A036242 A036243 A036244
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description and more terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 02 2001
Edited by and terms a(30) to a(41) from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 21 2003
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