A126428 a(1) = 1; for n > 1, a(n) = smallest number > a(n-1) such that pairwise sums and (absolute) differences of distinct elements are all distinct.

1, 2, 6, 12, 21, 37, 58, 84, 112, 129, 173, 213, 266, 307, 373, 446, 513, 589, 639, 829, 916, 1061, 1209, 1297, 1429, 1461, 1626, 1783, 1964, 2220, 2576, 2653, 2875, 3064, 3307, 3605, 3889, 4228, 4332, 4412, 4658, 5337, 5618, 5647, 6281, 6511, 7001, 7388

Offset: 1

Author

Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Mar 11 2007, Jul 27 2007

Keywords

• nonn

Examples

			a(1) = 1, a(2) = 2; n = 3: k = 3, k-a(2) = 1 = a(2)-a(1), so a(3) > 3; k = 4: k-a(1) = 3 = a(1)+a(2), so a(3) > 4; k = 5: k-a(2) = 3 = a(1)+a(2), so a(3) > 5; k=6: k-a(1) = 5, k-a(2) = 4, k+a(1) = 7, k+a(2) = 8, a(2)-a(1) = 1, a(2)+a(1) = 3 are all distinct, hence a(3) = 6.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..2000
• Eric Weisstein's World of Mathematics, B2-Sequence
• Index entries for B_2 sequences

Crossrefs

Cf. A005282 (Mian-Chowla sequence).

Programs

Haskell

import Data.List (intersect)
a126428 n = a126428_list !! (n-1)
a126428_list =  magics 1 [] [] where
   magics :: Integer -> [Integer] -> [Integer] -> [Integer]
   magics n ms tests
      | tests `intersect` nMinus == [] && tests `intersect` nPlus == []
      = n : magics (n+1) (n:ms) (nMinus ++ nPlus ++ tests)
      | otherwise
      = magics (n+1) ms tests
      where nMinus = map (n -) ms
            nPlus  = map (n +) ms
-- magics is the generator for a004210_list, cf. A004210, magic integers.
-- Reinhard Zumkeller, Mar 03 2011

PARI

{m=48; u=[]; s=Set(); k=0; for(n=1, m, b=1; while(b, b=0; k++; j=0; while(!b&&j<#u, j++; if(setsearch(s, k-u[j])||setsearch(s, k+u[j]), b=1))); print1(k, ","); if(n
				

Extensions

Edited and extended by Klaus Brockhaus, Sep 05 2007