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.

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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.

Crossrefs

Cf. A060470.

Programs

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

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 *)

Extensions

Name edited by Michel Marcus, Dec 11 2017