A240277 Minimal number of people such that exactly n days are required to spread gossip.

1, 2, 4, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297

Offset

0,2

Comments

A007456(a(n)) = n and A007456(m) < n for m < a(n);

for n > 2: a(n) = 2^(n-2) + 1, cf. A000051.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Chai Wah Wu, May 18 2017: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) for n > 4.

G.f.: (4*x^4 - 5*x^3 - x + 1)/((x - 1)*(2*x - 1)). (End)

E.g.f.: (4*x^2 + 2*x + exp(x)*(exp(x) + 4) - 1)/4. - Stefano Spezia, Jul 03 2024

Mathematica

Join[{1, 2, 4}, 2^Range[50] + 1] (* or *)
LinearRecurrence[{3, -2}, {1, 2, 4, 3, 5}, 50] (* Paolo Xausa, Jul 02 2024 *)

Prog

(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a240277 = (+ 1) . fromJust . (`elemIndex` a007456_list)

Crossrefs

Cf. A000051, A007456.

Sequence in context: A072799 A214928 A379649 * A091449 A100834 A264996

Adjacent sequences: A240274 A240275 A240276 * A240278 A240279 A240280

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 03 2014

Status

approved