cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A118066 Complement of A118065.

Original entry on oeis.org

8, 17, 24, 35, 40, 56, 72, 79, 92, 104, 108, 120, 124, 134, 142, 152, 176, 212, 226, 256, 269, 272, 286, 312, 324, 344, 353, 360, 456, 542, 548, 556, 592, 596, 644, 652, 689, 712, 748, 842, 884, 902, 968, 972, 988, 1012, 1016, 1097, 1168, 1193, 1246, 1256
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 11 2006

Keywords

Crossrefs

Cf. A048973.

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!

Original entry on oeis.org

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

Views

Author

D. R. Hofstadter, Jul 15 1977

Keywords

Comments

Most of the natural numbers are members. Conjecture: there are infinitely many nonmembers. Is there an estimate for a(k)/k ?
A118164(n) = number of representations of a(n) as sum of consecutive earlier terms. - Reinhard Zumkeller, Apr 13 2006

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

Crossrefs

Complement of A048973.
Cf. A118065, A118166.

Programs

  • 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

A124145 a(1)=1, a(2)=2, a(n)=smallest number greater than a(n-1) that can be written as sum of consecutive earlier terms in exactly one way.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 10, 16, 17, 18, 19, 22, 25, 26, 29, 32, 33, 37, 40, 41, 43, 45, 47, 48, 50, 54, 55, 57, 59, 62, 66, 67, 68, 69, 73, 75, 76, 77, 81, 83, 85, 86, 87, 95, 98, 99, 101, 105, 109, 117, 118, 120, 126, 128, 129, 131, 133, 134, 137, 139, 140, 141, 143, 146, 148
Offset: 1

Views

Author

Tobias Baumann (baumtobi(AT)students.uni-mainz.de), Dec 01 2006

Keywords

Comments

This sequence is similar to the Hofstadter sequence A005243 except the decomposition into summands has to be unique.
This sequence has similarities with Ulam numbers (A002858); here we consider unique sums of consecutive terms, there unique sums of two distinct terms. - Rémy Sigrist, Jan 02 2022

Examples

			a(7)=10 because 2+3+5=10 is the only way to sum up consecutive terms. 11 is not contained in the sequence because 11=5+6=1+2+3+5 has got more than one decompositions.

Links

Crossrefs

Cf. A002858, A005243, A118065, A118164, A118166.

Programs

  • PARI
    See Links section.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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