A182113 Lexicographically earliest permutation of the positive integers such that a(n+a(n)+1) has the same parity as a(n).

1, 2, 3, 4, 6, 7, 5, 8, 10, 11, 9, 12, 13, 15, 16, 14, 18, 19, 17, 20, 21, 23, 24, 22, 26, 27, 25, 28, 29, 31, 32, 30, 33, 34, 35, 36, 37, 39, 40, 38, 42, 43, 41, 44, 45, 47, 48, 46, 49, 50, 51, 52, 53, 55, 56, 54, 58, 59, 57, 60, 61, 63, 64, 62, 65, 66, 67, 68, 70, 71, 69, 72, 74, 75, 73

Offset

1,2

Comments

a(n+a(n)+1) is the term reached by "jumping over" a(n) terms to the right of a(n).

Links

Table of n, a(n) for n=1..75.

E. Angelini, Small perturbations in the natural flow, SeqFan list, Apr 12 2012

Example

a(1)=1 means that jumping over its neighbor we will land on a(3) which must have the same parity as a(1).
a(2)=2 means that jumping over a(3), a(4), we will land on a(5) which must be even, as is a(2). Therefore a(5) cannot equal 5 (which would be the least available number not yet used), the least possible choice is a(5)=6 (after having filled in a(3) with the least unused odd number, and a(4) with the least unused number without restriction).

Prog

(PARI) {R=vector(222); u=0; for(n=1, 100, a=0; while( bittest(u, a++) || (R[n] &(a+R[n])%2) || (R[n+a+1] & (a+R[n+a+1])%2), ); u+=1<<R[n]=a; R[n+a+1]=bittest(a, 0)-2); vecextract(R, "1..100")}

Crossrefs

Sequence in context: A071666 A026264 A073208 * A361647 A354901 A026236

Adjacent sequences: A182110 A182111 A182112 * A182114 A182115 A182116

Keyword

nonn

Author

Eric Angelini and M. F. Hasler, Apr 12 2012

Status

approved