A353035 a(n) = A119435(2^n).

1, 2, 3, 4, 6, 8, 11, 15, 20, 27, 36, 48, 64, 85, 116, 153, 208, 273, 366, 493, 649, 888, 1161, 1579, 2092, 2784, 3783, 4946, 6772, 8875, 11977, 16065, 21193, 28979, 37823, 51633, 68117, 91045, 123377, 161622, 221441, 289493, 392259, 523328, 692771, 945393

Offset: 0

Author

Michael De Vlieger, Apr 18 2022

Keywords

• nonn
• base

Comments

Local minima of A119435.

Let U(n,j) be the j-th smallest missing number in A119435(1..n-1). Example: for A119435(1..11), U(12,j) begins {6, 8, 10, 11, 14, ...}. Therefore we may alternatively define A119435(n) = U(n, A030101(n)).

Theorem: A119435(2^k) represents a local minimum. Proof: Observe that A030101(2^k) = 1. 2^k expressed in binary is 1 followed by zeros. When we reverse this number, the leading zeros are trivial and we read the number 1 in the 2^0 place. Therefore we select U(2^k, 1), which is the smallest missing number in A119435(1..n-1). Hence, a(n) = A119435(2^n).

Also positions of 2^n in A119436.

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A030101, A119435, A119436.

Programs

Mathematica

a = {1}; nn = 2^14; Do[AppendTo[a, Complement[Range[i + 2 nn], a][[IntegerReverse[i, 2]] ]], {i, 2, nn}]; Array[a[[2^#]] &, Floor@ Log2@ Length@ a - 1, 0]

PARI

\\ See Links section.

Extensions

More terms from Rémy Sigrist, Apr 19 2022