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A052463 a(n) is the smallest nonnegative solution k to 24k == 1 (mod 7^(2n-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.

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.

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 *)

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. 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

Eric W. Weisstein

EXTENSIONS

Name edited by Petros Hadjicostas, Oct 09 2019

STATUS

approved

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Last modified January 17 18:14 EST 2020. Contains 330987 sequences. (Running on oeis4.)