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 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) 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 S. R. Finch, Ulam s-Additive Sequences 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 A018293 Adjacent sequences:  A003041 A003042 A003043 * A003045 A003046 A003047 KEYWORD nonn,nice AUTHOR EXTENSIONS Name edited by Michel Marcus, Dec 11 2017 STATUS approved

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)