A072009 -id:A072009 - cp's OEIS frontend

A072007 a(0) = 0; for n>=1, a(n)=least nonnegative integer x such that |x-a(n-1)|>=n and x is not a(k) for any k

0, 1, 3, 6, 2, 7, 13, 4, 12, 21, 5, 16, 28, 8, 22, 37, 9, 26, 44, 10, 30, 51, 11, 34, 58, 14, 40, 67, 15, 45, 75, 17, 49, 82, 18, 53, 89, 19, 57, 96, 20, 61, 103, 23, 68, 113, 24, 71, 119, 25, 76, 127, 27, 80, 134, 29, 85, 142, 31, 90, 150, 32

Offset: 0

Clark Kimberling, Jun 07 2002

nonn

A permutation of the nonnegative integers.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A072008, A072009 (inverse).

import Data.List (delete)
a072007 n = a072007_list !! n
a072007_list = 0 : f 1 0 [1..] where
   f u v ws = g ws where
     g (x:xs) = if abs (x - v) < u
                   then g xs else x : f (u + 1) x (delete x ws)
-- Reinhard Zumkeller, Sep 04 2014

A167046 Angry numbers: each number n must be more than n places from n-1 and n+1. This sequence places each number as early as possible.

Original entry on oeis.org

1, 4, 7, 2, 10, 13, 16, 3, 5, 19, 22, 8, 25, 28, 31, 6, 11, 34, 37, 40, 14, 9, 43, 46, 17, 49, 52, 55, 58, 12, 20, 61, 64, 67, 23, 70, 15, 73, 76, 26, 79, 82, 85, 18, 29, 88, 91, 32, 94, 97, 100, 103, 21, 35, 106, 109, 112, 38, 115, 24, 118, 41, 121, 124, 127, 130, 133, 27

Offset: 1

Franklin T. Adams-Watters, Oct 27 2009

nonn

This sequence is a permutation of the positive integers. After any two increases in the position of n from after the first hole, it will be possible to put the next number in that hole.

			For a(n) = 2, n must be at least 3 away from a^{-1}(1) = 1, so n = 4. Next, a(n) = 3 must be 4 away from 4, so it can't be less than 4; hence a(8) = 3. Then a(n) = 4 must be 5 away from 8; the first hole at 2 is far enough, so a(2) = 4.

Cf. A072009, A065187, A167048, A167047

dist(n) = n+1
al(n) = {local(d,v,w,mn,j);
v=vector(n);w=vector(n);
v[1]=w[1]=1;mn=2;
for(k=2,n,
d=dist(k);
if(w[k-1]-d>=mn,
j=mn;mn++;while(v[mn],mn++),
j=w[k-1]+d;while(j<=#v&v[j],j++);if(j>#v,v=vector(j,i,if(i<=#v,v[i],0))));
v[j]=k;w[k]=j);
v}

cp's OEIS Frontend

A072007 a(0) = 0; for n>=1, a(n)=least nonnegative integer x such that |x-a(n-1)|>=n and x is not a(k) for any k

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell