A003044 For n > 4, a(n) is the least integer > a(n-1) with precisely two representations a(n) = a(i) + a(j), 1 <= i < j < n; and a(n) = n for n=1..4. (Formerly M0506)

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 19, 29, 31, 33, 43, 44, 47, 51, 54, 58, 68, 69, 78, 79, 86, 95, 99, 110, 113, 117, 133, 134, 135, 145, 151, 156, 159, 173, 180, 183, 193, 197, 204, 211, 229, 232, 236, 239, 243, 250, 256, 264, 270, 281, 284

Offset

1,2

Comments

First differs from A060470 at a(13) = 29. - Peter Munn, Dec 10 2017

References

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 145-151.

R. K. Guy, Unsolved Problems in Number Theory, Section C4.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..5440

Steven R. Finch, Ulam s-Additive Sequences [From Steven Finch, Apr 20 2019]

R. Queneau, Sur les suites s-additives, J. Combin. Theory, A12 (1972), 31-71. Queneau left out 44.

Mathematica

a[n_ /; n <= 4] = n; a[n_] := a[n] = Catch[ For[an = a[n-1] + 1, True, an++, cnt = 0; Do[If[an == a[i] + a[j], cnt++], {i, 1, n-1}, {j, i+1, n-1}]; If[cnt == 2, Throw[an]]]]; Table[a[n], {n, 1, 56}](* Jean-François Alcover, Apr 30 2012 *)

Prog

(Haskell)
a003044 n = a003044_list !! (n-1)
a003044_list = 1 : 2 : 3 : 4 : f [4, 3..1] where
   f xs@(x:_) = y : f (y : xs) where
     y = head [w | w <- [x + 1 ..],
         length [() | v <- xs, (w - v) `elem` dropWhile (>= v) xs] == 2]
-- Reinhard Zumkeller, Mar 17 2013

Crossrefs

Cf. A060470.

Sequence in context: A018350 A033058 A060470 * A279077 A018541 A361785

Adjacent sequences: A003041 A003042 A003043 * A003045 A003046 A003047

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Name edited by Michel Marcus, Dec 11 2017

Status

approved