A256210 Lexicographically earliest permutation of positive integers starting with 2 such that a(a(n)+a(n+1)) is odd for all n.

2, 1, 3, 5, 4, 6, 7, 9, 11, 13, 8, 10, 15, 12, 14, 17, 16, 19, 18, 21, 23, 20, 22, 25, 27, 29, 31, 24, 26, 28, 33, 30, 35, 32, 37, 34, 39, 36, 41, 38, 40, 43, 45, 47, 42, 44, 49, 46, 48, 51, 50, 53, 52, 55, 57, 59, 54, 56, 58, 61, 63, 60, 65, 62, 67, 64, 69

Offset: 1

Author

N. J. A. Sloane, Mar 26 2015

Keywords

• nonn

Comments

This is the sequence U defined in the comments on A255003.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A255003.

Cf. A256371 (inverse), A256372 (fixed points).

Programs

Haskell

after Robert Israel's Maple program
import Data.IntSet (empty, member, insert)
a256210 n = a256210_list !! (n-1)
a256210_list = 2 : f [2 ..] 2 [1, 3 ..] [4, 6 ..] empty where
   f (x:xs) y us'@(u:us) vs'@(v:vs) s
     | member x s || u < v = u : f xs u us vs' (insert (y + u) s)
     | otherwise           = v : f xs v us' vs (insert (y + v) s)
-- Reinhard Zumkeller, Mar 26 2015

Maple

N:= 100: # to get a(n) for n <= N
maxodd:= -1:
maxeven:= 2:
a[1]:= 2:
needodd:= {}:
for n from 2 to N do
  if member(n,needodd) or maxodd < maxeven then
     a[n]:= maxodd + 2;
     maxodd:= a[n];
  else
     a[n]:= maxeven + 2;
     maxeven:= a[n];
  fi;
  needodd:= needodd union {a[n-1]+a[n]};
od:
seq(a[n],n=1..N); # Robert Israel, Mar 26 2015

Mathematica

nn = 100;
maxodd = -1;
maxeven = 2;
a[1] = 2;
needodd = {};
For[n = 2, n <= nn, n++,
    If[MemberQ[needodd, n] || maxodd < maxeven,
       a[n] = maxodd + 2;
       maxodd = a[n]
   ,
       a[n] = maxeven + 2;
       maxeven = a[n]
   ];
    needodd = needodd ~Union~ {a[n-1]+a[n]};
];
Array[a, nn] (* Jean-François Alcover, Aug 04 2018, after Robert Israel *)