A332072 The Blue Comma sequence: Differences of indices of even terms gives back the sequence; lexicographically earliest such permutation of positive integers.

1, 2, 4, 3, 6, 5, 7, 9, 8, 11, 13, 10, 15, 17, 19, 21, 23, 12, 25, 27, 29, 31, 14, 33, 35, 37, 39, 41, 43, 16, 45, 47, 49, 51, 53, 55, 57, 59, 18, 61, 63, 65, 67, 69, 71, 73, 20, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 22, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 24, 119, 121, 123, 125, 127

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Eric Angelini, Yellow commas, pink, red, blue..., personal blog "Cinquante signes" on blogspot.com, May 17 2020

Example

The even terms are at indices 2, 3, 5, 9, 12, 18, 23, 30, ...; first differences give 1, 2, 4, 3, 6, 5, 7, ... = the sequence itself.

Prog

(PARI) upto(N)={my(a=Vec([1, 2], N), i=1, L=2); local(U=[2], nxt(e)=while(#U>1&&U[2]==U[1]+1, U=U[^1]); my(t=U[1]); until( t++%2!=e && !setsearch(U, t), ); U=setunion(U, [t]); t ); for(n=3, N, a[n]=nxt(n-L==a[i] && i++ && L=n)); a}

Crossrefs

Cf. A197756 (the Yellow Comma sequence: count digits between odd terms).

Sequence in context: A255552 A255551 A366949 * A330340 A328696 A053629

Adjacent sequences: A332069 A332070 A332071 * A332073 A332074 A332075

Keyword

nonn

Author

Eric Angelini and M. F. Hasler, May 19 2020

Status

approved