A003138 Nearest integer to 24*(2^n - 1)/n.

24, 36, 56, 90, 149, 252, 435, 765, 1363, 2455, 4466, 8190, 15122, 28085, 52427, 98303, 185041, 349524, 662257, 1258290, 2396744, 4575603, 8753329, 16777215, 32212254, 61946643, 119304646, 230087533

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

In case of a tie, round up. - N. J. A. Sloane, Nov 06 2022

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• R. J. Penrose, Puzzle, Twistor Newsletter, No. 10 (July 1980), p. 22.
• R. J. Penrose, Puzzle, Twistor Newsletter, No. 10 (July 1980), p. 22. [Cached copy]
• R. J. Penrose, Solution to puzzle, Twistor Newsletter, No. 41, p. 37, 1996.
• R. J. Penrose, Solution to puzzle, Twistor Newsletter, No. 41, p. 37, 1996. [Cached copy]
• Z. Sunic, Tree morphisms, transducers and integer sequences, arXiv:math/0612080 [math.CO], 2006.

Crossrefs

Cf. A003176, A003177, A121056.

Programs

Magma

[Round(24*(2^n -1)/n): n in [1..70]]; // G. C. Greubel, Nov 04 2022

Mathematica

A003138[n_]:= With[{m=24*(2^n-1)/n}, If[Floor[m+1/2] -Floor[m]>=1/2, Ceiling[m], Floor[m]]];
Table[A003138[n], {n,70}] (* G. C. Greubel, Nov 04 2022 *)

PARI

a(n) = round(24*(2^n - 1)/n); \\ Michel Marcus, Nov 05 2022

SageMath

[round(24*(2^n -1)/n) for n in range(1,71)] # G. C. Greubel, Nov 04 2022