A373112 Number of binary digits in the integer part of e^n.

2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 91, 93, 94, 96, 97, 99, 100, 101, 103, 104

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = floor(log_2(floor(e^n))) + 1.

a(n) = A070939(A000149(n)). - Michel Marcus, May 26 2024

Example

e^10 = 22026.46579480671... 22026 in binary is 101011000001010 so a(10)=15.

Mathematica

Table[IntegerLength[Floor[E^n], 2], {n, 80}] (* Harvey P. Dale, Nov 26 2025 *)

Crossrefs

Cf. A000149, A070939, A254528 (in decimal).

Sequence in context: A093001 A226721 A224996 * A246046 A026428 A030704

Adjacent sequences: A373109 A373110 A373111 * A373113 A373114 A373115

Keyword

nonn,base

Author

Byron Avery, May 25 2024

Status

approved