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A036241 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. 4
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; text; internal format)
OFFSET

1,2

REFERENCES

Letter from V. Jooste, Pretoria, South Africa, Sep. 8, 1975.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..75

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.

MATHEMATICA

a[1]=1; a[2]=2; a[3]=3; a[n_] := a[n] = Catch[For[an = a[n-1] + 1, True, an++, a[n] = an; t2 = Flatten[Table[a[i] + a[j], {i, 1, n}, {j, i+1, n}]]; If[n*(n-1)/2 == Length[Union[t2]], t3 = Flatten[Table[a[i] + a[j] + a[k], {i, 1, n}, {j, i+1, n}, {k, j+1, n}]]; If[ n*(n-1)*(n-2)/6 == Length[Union[t3]], Throw[an]]]]]; Table[Print[a[n]]; a[n], {n, 1, 41}] (* Jean-François Alcover, Jul 24 2012 *)

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

CROSSREFS

Cf. A062065, A051912, A060276.

Sequence in context: A091956 A107480 A128021 * A192633 A125028 A119262

Adjacent sequences:  A036238 A036239 A036240 * A036242 A036243 A036244

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Better description and more terms from Naohiro Nomoto, Jul 02 2001

Edited by and terms a(30) to a(41) from Klaus Brockhaus, May 21 2003

STATUS

approved

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Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)