A375301 Triangle T(n,k) read by rows with row n equal to the unique permutation pi_n of [1, ..., n] such that k + pi_n(k) is a power of 2 for 1 <= k <= n.

1, 1, 2, 3, 2, 1, 3, 2, 1, 4, 1, 2, 5, 4, 3, 1, 6, 5, 4, 3, 2, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 8, 1, 6, 5, 4, 3, 2, 9, 8, 7, 1, 2, 5, 4, 3, 10, 9, 8, 7, 6, 3, 2, 1, 4, 11, 10, 9, 8, 7, 6, 5, 3, 2, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 1, 2, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3

Offset

1,3

Links

Table of n, a(n) for n=1..91.

Zhi-Wei Sun, On permutations of {1, ..., n} and related topics, J Algebr Comb 54, 893-912 (2021); Theorem 1.2, page 895.

Example

The triangle begins
  1,
  1, 2,
  3, 2, 1,
  3, 2, 1, 4,
  1, 2, 5, 4, 3,
  1, 6, 5, 4, 3, 2,
  7, 6, 5, 4, 3, 2, 1,
  7, 6, 5, 4, 3, 2, 1, 8,
  ...
Row 5: [1, 2, 5, 4, 3] + [1, 2, 3, 4, 5] = [2, 4, 8, 8, 8]; only powers of 2 in the vector of sums.

Prog

(PARI) a375301_row(n) = forperm(n, p, my(f=1); for(k=1, n, my(s=p[k]+k); if(2^valuation(s, 2)!=s, f=0; break)); if(f==1, return(Vec(p))))

Crossrefs

A375302 gives the rank of row n in lexicographically ordered permutations of [n].

Cf. A000079.

Sequence in context: A204933 A240224 A118105 * A125211 A139367 A117648

Adjacent sequences: A375298 A375299 A375300 * A375302 A375303 A375304

Keyword

nonn,tabl

Author

Hugo Pfoertner, Aug 25 2024

Status

approved