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

%I A240277 #23 Jul 03 2024 12:46:59
%S A240277 1,2,4,3,5,9,17,33,65,129,257,513,1025,2049,4097,8193,16385,32769,
%T A240277 65537,131073,262145,524289,1048577,2097153,4194305,8388609,16777217,
%U A240277 33554433,67108865,134217729,268435457,536870913,1073741825,2147483649,4294967297
%N A240277 Minimal number of people such that exactly n days are required to spread gossip.
%C A240277 A007456(a(n)) = n and A007456(m) < n for m < a(n);
%C A240277 for n > 2: a(n) = 2^(n-2) + 1, cf. A000051.
%H A240277 Paolo Xausa, <a href="/A240277/b240277.txt">Table of n, a(n) for n = 0..1000</a>
%H A240277 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A240277 From _Chai Wah Wu_, May 18 2017: (Start)
%F A240277 a(n) = 3*a(n-1) - 2*a(n-2) for n > 4.
%F A240277 G.f.: (4*x^4 - 5*x^3 - x + 1)/((x - 1)*(2*x - 1)). (End)
%F A240277 E.g.f.: (4*x^2 + 2*x + exp(x)*(exp(x) + 4) - 1)/4. - _Stefano Spezia_, Jul 03 2024
%t A240277 Join[{1, 2, 4}, 2^Range[50] + 1] (* or *)
%t A240277 LinearRecurrence[{3, -2}, {1, 2, 4, 3, 5}, 50] (* _Paolo Xausa_, Jul 02 2024 *)
%o A240277 (Haskell)
%o A240277 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A240277 a240277 = (+ 1) . fromJust . (`elemIndex` a007456_list)
%Y A240277 Cf. A000051, A007456.
%K A240277 nonn,easy
%O A240277 0,2
%A A240277 _Reinhard Zumkeller_, Apr 03 2014