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A052465 a(n) is the solution k to Mod[24k,11^n]==1. 5
6, 116, 721, 14031, 87236, 1697746, 10555551, 205427261, 1277221666, 24856698576, 154543821581, 3007660527691, 18699802411296, 363926923850606, 2262676091766811, 44035157785923321 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Related to a Ramanujan congruence for the partition function P.

REFERENCES

G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), Volume 1 Issue 6, December 2014, ISSN: 2349-8862; http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..900

Eric Weisstein's World of Mathematics, Partition Function Congruences.

Index entries for linear recurrences with constant coefficients, signature (1,121,-121).

FORMULA

G.f.: x*(-121*x^2+110*x+6)/((1-x)*(1-121*x^2)). - Vincenzo Librandi, Jul 01 2012

a(n) = a(n-1) +121*a(n-2) -121*a(n-3). - Vincenzo Librandi, Jul 01 2012

MATHEMATICA

Table[PowerMod[24, -1, 11^c], {c, 20}]

CoefficientList[Series[(-121x^2+110x+6)/((1-x)(1-121*x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 01 2012 *)

LinearRecurrence[{1, 121, -121}, {6, 116, 721}, 20] (* Harvey P. Dale, Apr 27 2014 *)

PROG

(MAGMA) I:=[6, 116, 721]; [n le 3 select I[n] else Self(n-1)+121*Self(n-2)-121*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 01 2012

CROSSREFS

Cf. A052462, A052463, A052466.

Sequence in context: A317172 A278752 A003425 * A229582 A113015 A024275

Adjacent sequences:  A052462 A052463 A052464 * A052466 A052467 A052468

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)