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

Author

Reinhard Zumkeller, Apr 03 2014

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000051, A007456.

Programs

Haskell

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

Mathematica

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

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