A379175 Irregular triangle T(n, k), n >= 0, k = 1..ceiling(2^(A007895(n)-1)); the n-th row lists the nonnegative integers m such that A184617(m) = A003714(n).

0, 1, 2, 4, 3, 5, 8, 7, 9, 6, 10, 16, 15, 17, 14, 18, 12, 20, 11, 13, 19, 21, 32, 31, 33, 30, 34, 28, 36, 27, 29, 35, 37, 24, 40, 23, 25, 39, 41, 22, 26, 38, 42, 64, 63, 65, 62, 66, 60, 68, 59, 61, 67, 69, 56, 72, 55, 57, 71, 73, 54, 58, 70, 74, 48, 80, 47, 49, 79, 81

Offset: 0

Author

Rémy Sigrist, Dec 17 2024

Keywords

• nonn
• tabf
• base

Comments

Also the nonnegative terms of A379147, in order of appearance.

This sequence is a permutation of the nonnegative integers with inverse A379176.

This sequence shares graphical features with A368225.

Examples

			Triangle T(n, k) begins:
  n   n-th row
  --  --------------
   0  0
   1  1
   2  2
   3  4
   4  3, 5
   5  8
   6  7, 9
   7  6, 10
   8  16
   9  15, 17
  10  14, 18
  11  12, 20
  12  11, 13, 19, 21
  13  32
  14  31, 33
  15  30, 34
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10922 (rows for n = 0..986 flattened)
• Index entries for sequences related to Zeckendorf expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A003714, A007895, A184617, A368225, A379147, A379176 (inverse).

Programs

PARI

tozeck(n) = { for (i=0, oo, if (n<=fibonacci(2+i), my (v=0, f); forstep (j=i, 0, -1, if (n>=f=fibonacci(2+j), n-=f; v+=2^j;); if (n==0, return (v););););); }
row(n) = { my (z = tozeck(n), r = [0], b); while (z, z -= b = 2^valuation(z, 2); r = concat([v - b | v <- r], [v + b | v <- r]);); return (select(v -> v >= 0, r)); }

Formula

T(n, ceiling(2^(A007895(n)-1))) = A003714(n).