%I #12 Feb 15 2015 00:52:02
%S 5,8,10,24,28,33,37,40,46,63,69,70,83,85,94,95,102,105,106,112,113,
%T 114,119,131,145,147,148,152,161,165,166,175,181,197,203,207,215,221,
%U 235,236,239,247,253,254,267,270,276,286,289,290,296,307,309,315,317,322
%N Construct difference array so that (1) first row begins with 1, (2) every row is monotonic increasing, (3) no number appears more than once, (4) smallest number not yet used begins a new row. Sequence gives numbers not used.
%H Reinhard Zumkeller, <a href="/A057154/b057154.txt">Table of n, a(n) for n = 1..514</a>
%e Array begins
%e 1 3 9 26 73 194 ...
%e .2 6 17 47 121 ...
%e . 4 11 30 74 ...
%e .. 7 19 44 ...
%e ... 12 25 ...
%e .... 13 ...
%o (Haskell)
%o import Data.List (intersect, union, (\\))
%o a057154 n = a057154_list !! (n-1)
%o a057154_list = g [1] [2..] [1] where
%o g ds (a:as) us
%o | null (ds' `intersect` us) = g ds' (as \\ ds') (us `union` ds')
%o | otherwise = a : g ds as us
%o where ds' = scanl (+) a ds
%o -- _Reinhard Zumkeller_, Nov 19 2011
%Y Cf. A057153 (first row), A052474 (main diagonal), A056230 (array), A056231, A056232, A056233, A056234.
%K nice,nonn,easy
%O 1,1
%A _Jonas Wallgren_, Jul 30 2000
%E More terms from Rob Speer (rob(AT)twcny.rr.com) and Loren Merritt, Aug 14 2000
%E Further terms from Larry Reeves (larryr(AT)acm.org), May 09 2001