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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.

%I A126428 #17 Feb 16 2025 08:33:04
%S A126428 1,2,6,12,21,37,58,84,112,129,173,213,266,307,373,446,513,589,639,829,
%T A126428 916,1061,1209,1297,1429,1461,1626,1783,1964,2220,2576,2653,2875,3064,
%U A126428 3307,3605,3889,4228,4332,4412,4658,5337,5618,5647,6281,6511,7001,7388
%N 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.
%H A126428 Klaus Brockhaus, <a href="/A126428/b126428.txt">Table of n, a(n) for n = 1..2000</a>
%H A126428 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/B2-Sequence.html">B2-Sequence</a>
%H A126428 <a href="/index/Br#B_2">Index entries for B_2 sequences</a>
%e A126428 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.
%o A126428 (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<m, v=vector(#u, j, k-u[j]); w=vector(#u, j, k+u[j]); s=setunion(s, Set(concat(v, w))); u=concat(u, k)))} /* Klaus Brockhaus, Sep 05 2007 */
%o A126428 (Haskell)
%o A126428 import Data.List (intersect)
%o A126428 a126428 n = a126428_list !! (n-1)
%o A126428 a126428_list =  magics 1 [] [] where
%o A126428    magics :: Integer -> [Integer] -> [Integer] -> [Integer]
%o A126428    magics n ms tests
%o A126428       | tests `intersect` nMinus == [] && tests `intersect` nPlus == []
%o A126428       = n : magics (n+1) (n:ms) (nMinus ++ nPlus ++ tests)
%o A126428       | otherwise
%o A126428       = magics (n+1) ms tests
%o A126428       where nMinus = map (n -) ms
%o A126428             nPlus  = map (n +) ms
%o A126428 -- magics is the generator for a004210_list, cf. A004210, magic integers.
%o A126428 -- _Reinhard Zumkeller_, Mar 03 2011
%Y A126428 Cf. A005282 (Mian-Chowla sequence).
%K A126428 nonn
%O A126428 1,2
%A A126428 Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Mar 11 2007, Jul 27 2007
%E A126428 Edited and extended by _Klaus Brockhaus_, Sep 05 2007