

A035311


First column of the Zorach additive triangle A035312.


9



1, 2, 4, 7, 5, 8, 10, 14, 15, 19, 16, 20, 21, 22, 27, 30, 28, 33, 32, 38, 37, 39, 44, 45, 51, 46, 47, 54, 55, 52, 59, 62, 60, 64, 50, 67, 72, 78, 74, 68, 81, 82, 80, 85, 79, 87, 86, 91, 90, 94, 102, 98, 103, 99, 105, 100, 108, 112, 110, 113, 127, 128, 125, 133, 118, 123
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OFFSET

0,2


COMMENTS

One can see that (least unused number in rows 1 through n of A035312) ~ A035311(n) ~ 2n. (Asymptotic equality, and the first quantity does not exceed either of the two others.)  M. F. Hasler, May 09 2013


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
A. C. Zorach, Additive triangle
Haskell programs for sequences in connection with Zorach additive triangle


MATHEMATICA

(* Assuming n <= t(n, 1) <= 3n *) uniqueQ[t1_, n_] := (t[n, 1] = t1; Do[t[n, k] = t[n, k1] + t[n1, k1], {k, 2, n}]; n*(n+1)/2 == Length[ Union[ Flatten[ Table[ t[m, k], {m, 1, n}, {k, 1, m}]]]]); t[n_ , 1] := t[n, 1] = Select[ Complement[ Range[n, 3 n], Flatten[ Table[t[m, k], {m, 1, n  1}, {k, 1, m}]]], uniqueQ[#, n] & , 1][[1]]; Table[t[n, 1], {n, 1, 66}](* JeanFrançois Alcover, Dec 02 2011 *)


PROG

See link for Haskell program.


CROSSREFS

Cf. A035312, A035313, A189713, A035358.
Sequence in context: A011178 A136790 A073158 * A182310 A244591 A299324
Adjacent sequences: A035308 A035309 A035310 * A035312 A035313 A035314


KEYWORD

nonn,easy,nice


AUTHOR

Alex Zorach


EXTENSIONS

More terms from Christian G. Bower


STATUS

approved



