A383180 Irregular table T(n,k) = A010846(A019565(2^n + k)).

1, 2, 2, 5, 2, 6, 5, 18, 2, 6, 5, 19, 5, 20, 16, 68, 2, 7, 6, 22, 5, 21, 18, 77, 5, 22, 17, 79, 16, 74, 60, 283, 2, 7, 6, 23, 5, 23, 18, 80, 5, 22, 18, 82, 16, 78, 62, 295, 5, 24, 19, 87, 16, 82, 64, 315, 15, 80, 62, 316, 55, 290, 226, 1161

Offset: 0

Author

Michael De Vlieger, May 09 2025

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  0: 1;
  1: 2;
  2: 2, 5;
  3: 2, 6, 5, 18;
  4: 2, 6, 5, 19, 5, 20, 16, 68;
  5: 2, 7, 6, 22, 5, 21, 18, 77, 5, 22, 17, 79, 16, 74, 60, 283;
   ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..16384 (rows n = 0..14, flattened)
• Michael De Vlieger, Log log scatterplot of a(n), n = 0..2^14.
• Michael De Vlieger, Fan style binary tree showing a(n) for n = 0..14, with a color function showing smaller numbers in reds and oranges, larger numbers in blues and magentas.

Crossrefs

Cf. A005117, A010846, A019565, A363061.

Programs

Mathematica

(* Load the "theta" program at the Mathematica link in A369609, then: *)
f[x_] := Times @@ Prime@ Position[Reverse@ IntegerDigits[x, 2], 1][[All, 1]]; Table[theta[f[2^n + k] ], {n, 0, 7}, {k, 0, 2^n - 1}]

Formula

T(0,0) = 1.

T(n,0) = 2.

T(n,2^(n-1)-1) = A363061(n).