A005243 A self-generating sequence: start with 1 and 2, take all sums of any number of successive previous elements and adjoin them to the sequence. Repeat!
1, 2, 3, 5, 6, 8, 10, 11, 14, 16, 17, 18, 19, 21, 22, 24, 25, 29, 30, 32, 33, 34, 35, 37, 40, 41, 43, 45, 46, 47, 49, 51, 54, 57, 58, 59, 60, 62, 65, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100
Offset: 1
Examples
After 1,2,3,5,6 you can adjoin 8 = 3+5, 10 = 2+3+5, etc. 12 is not a term since it is not the sum of any set of consecutive previous terms.
References
- R. K. Guy, Unsolved Problems in Number Theory, E31.
- 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..1000
- Thomas Bloom, Problem 423, Erdős Problems.
- D. R. Hofstadter, Eta-Lore [Cached copy, with permission]
- D. R. Hofstadter, Pi-Mu Sequences [Cached copy, with permission]
- D. R. Hofstadter and N. J. A. Sloane, Correspondence, 1977 and 1991
- Eric Weisstein's World of Mathematics, Hofstadter Sequences.
Programs
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Haskell
import Data.Set (singleton, deleteFindMin, fromList, union, IntSet) a005243 n = a005243_list !! (n-1) a005243_list = 1 : h [1] (singleton 2) where h xs s = m : h (m:xs) (union s' $ fromList $ map (+ m) $ scanl1 (+) xs) where (m, s') = deleteFindMin s -- Reinhard Zumkeller, Dec 17 2015, Jun 22 2011 -
Mathematica
nmax = 200; For[ s = {1, 2}; n = 3, n <= nmax, n++, ls = Length[s]; tt = Total /@ Flatten[Table[s[[i ;; j]], {i, 1, ls-1}, {j, i+1, ls}], 1]; If[MemberQ[tt, n], AppendTo[s, n]]]; A005243 = s (* Jean-François Alcover, Oct 21 2016 *)
Extensions
More terms from Jud McCranie
Comments