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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A255003.

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

Sequence in context: A258654 A171085 A288538 * A256371 A064429 A234751

Adjacent sequences: A256207 A256208 A256209 * A256211 A256212 A256213

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2015

Status

approved