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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. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

EXAMPLE

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.

PROG

(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 */

(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

CROSSREFS

Cf. A005282 (Mian-Chowla sequence).

Sequence in context: A011892 A062482 A046960 * A187490 A147623 A232234

Adjacent sequences:  A126425 A126426 A126427 * A126429 A126430 A126431

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Edited and extended by Klaus Brockhaus, Sep 05 2007

STATUS

approved

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Last modified October 19 11:09 EDT 2019. Contains 328216 sequences. (Running on oeis4.)