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a(n) is the multiplicative inverse of 24 (mod 7^n).
1

%I #17 May 31 2021 21:51:04

%S 5,47,243,2301,11905,112747,583343,5524601,28583805,270705447,

%T 1400606443,13264566901,68629715705,649963778147,3362856069543,

%U 31848225129201,164779947407605,1560563031330847,8074217422972643,76467588535211501,395636653725659505,3746911838225363547,19386196032557315743

%N a(n) is the multiplicative inverse of 24 (mod 7^n).

%C 24 * a(n) == 1 (mod 7^n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ModularInverse.html">Modular Inverse</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,49,-49).

%F a(n) = (17*7^n+1)/24 for n odd; a(n) = (23*7^n+1)/24 for n even.

%F G.f.: x*(5 + 42*x - 49*x^2)/(1 - x - 49*x^2 + 49*x^3). - _Stefano Spezia_, May 12 2021

%e a(1) = 5 because 24 * 5 == 1 (mod 7^1).

%t LinearRecurrence[{1, 49, -49}, {5, 47, 243}, 23] (* _Amiram Eldar_, May 11 2021 *)

%o (PARI) a(n) = if(n%2 == 1, (17*7^n+1)/24, (23*7^n+1)/24);

%o (PARI) a(n) = lift(1/Mod(24,7^n)) \\ _Andrew Howroyd_, May 11 2021

%Y Cf. A340757, A340957, A344120.

%K nonn,easy

%O 1,1

%A _Washington Bomfim_, May 11 2021