A227617 -id:A227617 - cp's OEIS frontend

A227632 Record values in A227617.

1, 2, 5, 19, 34, 61, 114, 175, 1094, 1695, 3390, 9372, 15605, 116478, 220288, 455587, 552188

Offset: 1

Reinhard Zumkeller, Jul 19 2013

a227632 n = a227632_list !! (n-1)
(a227632_list, a227633_list) = unzip $ (1,1) : f 1 1 a227617_list where
   f i v (q:qs) | q > v = (q,i) : f (i + 1) q qs
                | otherwise = f (i + 1) v qs

A100707 a(1) = 1; for n > 1, a(n+1)=a(n)-k if there exists a positive number k (take the smallest) that has not yet been used and is such that a(n+1) is new and >0, otherwise a(n+1) = a(n)+k if the same conditions are satisfied.

Original entry on oeis.org

1, 2, 4, 7, 3, 8, 14, 6, 13, 22, 12, 23, 11, 24, 10, 25, 9, 26, 5, 27, 45, 21, 40, 20, 43, 18, 44, 17, 46, 16, 47, 19, 51, 15, 48, 82, 42, 77, 39, 76, 37, 78, 36, 79, 35, 80, 34, 81, 33, 83, 32, 84, 31, 85, 30, 86, 29, 87, 38, 97, 28, 88, 149, 75, 137, 74

Offset: 1

N. J. A. Sloane and Vinay Vaishampayan, Dec 10 2004

A sequence of distinct natural numbers with the property that absolute successive differences are distinct.
A more long-winded definition: start with a(1) = 1. We keep a list of the numbers k that have been used as differences so far; initially this list is empty. Each difference can be used at most once.
Suppose a(n) = M. To get a(n+1), we subtract from M each number k < M that has not yet been used, starting from the smallest. If for any such k, M-k is a number not yet in the sequence, set a(n+1) = M-k and mark the difference k as used.
If no k works, then we add each number k that has not yet been used to M, again starting with the smallest. When we find a k such that M+k is a number not yet in the sequence, we set a(n+1) = M+k and mark k as used. Repeat.
The main question is: does every number appear in the sequence?
A227617(n) = smallest m such that a(m) = n: if this sequence is a permutation of the natural numbers, then A227617 is its inverse. - Reinhard Zumkeller, Jul 19 2013

			1 -> 1+1 = 2 and k=1 has been used as a difference.
2 -> 2+4 = 4 and k=2 has been used as a difference.
4 could go to 4-3 = 1, except that 1 has already appeared in the sequence; so 4 -> 4+3 = 7 and k=3 has been used as a difference.
7 -> 7-4 = 3 (for the first time we can subtract) and k=4 has been used as a difference. And so on.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Similar to Murthy's sequence A093903, Cald's sequence (A006509) and Recamán's sequence A005132. See also A081145, A100709 (another version). Cf. A100708 (the successive differences associated with this sequence).

import Data.List (delete)
import qualified Data.Set as Set (insert)
import Data.Set (singleton, member)
a100707 n = a100707_list !! (n-1)
a100707_list = 1 : f 1 (singleton 1) [1..] where
   f y st ds = g ds where
     g (k:ks) | v <= 0      = h ds
              | member v st = g ks
              | otherwise   = v : f v (Set.insert v st) (delete k ds)
              where v = y - k
     h (k:ks) | member w st = h ks
              | otherwise   = w : f w (Set.insert w st) (delete k ds)
              where w = y + k
-- Reinhard Zumkeller, Jul 19 2013

Data corrected for n > 46 by Reinhard Zumkeller, Jul 19 2013

cp's OEIS Frontend

A227632 Record values in A227617.

Views

Author

Keywords

Comments

Programs

Haskell

A227633 Where record values occur in A227617.

Views

Author

Keywords

Comments

Programs

Haskell

A100707 a(1) = 1; for n > 1, a(n+1)=a(n)-k if there exists a positive number k (take the smallest) that has not yet been used and is such that a(n+1) is new and >0, otherwise a(n+1) = a(n)+k if the same conditions are satisfied.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Extensions