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A240277
Minimal number of people such that exactly n days are required to spread gossip.
2
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.
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
Sequence in context: A082329 A072799 A214928 * A091449 A100834 A264996
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Apr 03 2014
STATUS
approved