A057154 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.

5, 8, 10, 24, 28, 33, 37, 40, 46, 63, 69, 70, 83, 85, 94, 95, 102, 105, 106, 112, 113, 114, 119, 131, 145, 147, 148, 152, 161, 165, 166, 175, 181, 197, 203, 207, 215, 221, 235, 236, 239, 247, 253, 254, 267, 270, 276, 286, 289, 290, 296, 307, 309, 315, 317, 322

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..514

Example

Array begins
1 3 9 26 73 194 ...
.2 6 17 47 121 ...
. 4 11 30 74 ...
.. 7 19 44 ...
... 12 25 ...
.... 13 ...

Prog

(Haskell)
import Data.List (intersect, union, (\\))
a057154 n = a057154_list !! (n-1)
a057154_list = g [1] [2..] [1] where
   g ds (a:as) us
     | null (ds' `intersect` us) = g ds' (as \\ ds') (us `union` ds')
     | otherwise = a : g ds as us
     where ds' = scanl (+) a ds
-- Reinhard Zumkeller, Nov 19 2011

Crossrefs

Cf. A057153 (first row), A052474 (main diagonal), A056230 (array), A056231, A056232, A056233, A056234.

Sequence in context: A157482 A314385 A185001 * A072524 A240968 A187878

Adjacent sequences: A057151 A057152 A057153 * A057155 A057156 A057157

Keyword

nice,nonn,easy

Author

Jonas Wallgren, Jul 30 2000

Extensions

More terms from Rob Speer (rob(AT)twcny.rr.com) and Loren Merritt, Aug 14 2000

Further terms from Larry Reeves (larryr(AT)acm.org), May 09 2001

Status

approved