The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A052463 a(n) is the smallest nonnegative solution k to 24*k == 1 (mod 7^(2*n-2)). 6
 0, 47, 2301, 112747, 5524601, 270705447, 13264566901, 649963778147, 31848225129201, 1560563031330847, 76467588535211501, 3746911838225363547, 183598680073042813801, 8996335323579097876247 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Related to a Ramanujan congruence for the partition function P = A000041. In other words, a(n) = k such that 24*k (mod 7^(2*n-2) ) == 1. - N. J. A. Sloane, Oct 08 2019 If b(n) = a(n) + 7^(2*n-2)*r, where r is a nonnegative integer, then there is an integer s >= 0 such that 24*b(n) = 24*a(n) + 24*7^(2*n-2)*r = 7^(2*n-2)*s + 1 + 24*7^(2*n-2)*r = 7^(2*n-2)*(24*r+s) + 1 == 1 (mod 7^(2*n-2)). Thus, we insist that a(n) is the smallest k >= 0 such that 24*k == 1 (mod 7^(2*n-2)). - Petros Hadjicostas, Oct 09 2019 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..600 G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), 1(6) (2014), ISSN: 2349-8862. Eric Weisstein's World of Mathematics, Partition Function P Congruences. Index entries for linear recurrences with constant coefficients, signature (50,-49). FORMULA G.f.: x^2*(-49*x + 47)/((1 - x)*(1 - 49*x)). a(n) = 49*a(n-1) - 2. - Vincenzo Librandi, Jul 01 2012 a(n) = 23*49^n/1176 + 1/24, n > 1. - R. J. Mathar, Oct 09 2019 MATHEMATICA Table[PowerMod[24, -1, 7^(2b-2)], {b, 20}] CoefficientList[Series[(-49x^2+47x)/((1-x)(1-49x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 01 2012 *) LinearRecurrence[{50, -49}, {0, 47, 2301}, 20] (* Harvey P. Dale, Aug 23 2021 *) PROG (MAGMA) I:=[0, 47]; [n le 2 select I[n] else 49*Self(n-1)-2: n in [1..20]]; // Vincenzo Librandi, Jul 01 2012 CROSSREFS Cf. A000041, A052462, A052465, A052466, A327770. Sequence in context: A218749 A049668 A009991 * A327770 A005148 A123798 Adjacent sequences:  A052460 A052461 A052462 * A052464 A052465 A052466 KEYWORD nonn,easy AUTHOR EXTENSIONS Name edited by Petros Hadjicostas, Oct 09 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 4 12:28 EDT 2022. Contains 355075 sequences. (Running on oeis4.)