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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-Fran├žois 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

N. J. A. Sloane

EXTENSIONS

Name edited by Michel Marcus, Dec 11 2017

STATUS

approved

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Last modified February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)