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

Author

Hugo Pfoertner, Aug 25 2024

Keywords

• nonn
• tabl

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A000079.

Programs

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))))