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A052462 a(n) is the solution k to Mod[24k,5^n]==1. 5


%S 4,24,99,599,2474,14974,61849,374349,1546224,9358724,38655599,

%T 233968099,966389974,5849202474,24159749349,146230061849,603993733724,

%U 3655751546224,15099843343099,91393788655599,377496083577474

%N a(n) is the solution k to Mod[24k,5^n]==1.

%C Related to a Ramanujan congruence for the partition function P.

%H Vincenzo Librandi, <a href="/A052462/b052462.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences.</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,25,-25).

%F G.f.: x(-25x^2+20x+4)/[(1-x)(1-5x)(1+5x)].

%F a(n) = (1+(21+2*(-1)^n)*5^n)/24 - Bruno Berselli, Apr 04 2011

%F a(n) = a(n-1) +25*a(n-2) -25*a(n-3). - _Vincenzo Librandi_, Jul 01 2012

%t Table[PowerMod[24, -1, 5^a], {a, 21}]

%t CoefficientList[Series[(-25x^2+20x+4)/((1-x)(1-5x)(1+5x)),{x,0,30}],x] (* _Vincenzo Librandi_, Jul 01 2012 *)

%o (MAGMA) I:=[4, 24, 99]; [n le 3 select I[n] else Self(n-1)+25*Self(n-2)-25*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jul 01 2012

%Y Cf. A052463, A052465, A052466.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_

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Last modified January 18 19:46 EST 2020. Contains 331030 sequences. (Running on oeis4.)