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%I #31 Jun 30 2021 02:33:42
%S 1,26,199,224,226,251,424,449,451,476,649,674,676,701,874,899,901,926,
%T 1099,1124,1126,1151,1324,1349,1351,1376,1549,1574,1576,1601,1774,
%U 1799,1801,1826,1999,2024,2026,2051,2224,2249,2251,2276,2449,2474,2476,2501
%N Numbers k such that k^14 == 1 (mod 15^2).
%C Numbers congruent to {1, 26, 129, 224} mod 225.
%H Amiram Eldar, <a href="/A056026/b056026.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Colin Barker)
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F G.f.: x*(1+25*x+173*x^2+25*x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F a(1)=1, a(2)=26, a(3)=199, a(4)=224, a(5)=226, a(n) = a(n-1)+a(n-4)-a(n-5). - _Harvey P. Dale_, Nov 11 2011
%F a(n) = (-225 - 125*(-1)^n + (171-171*i)*(-i)^n + (171+171*i)*i^n + 450*n)/8 where i=sqrt(-1). - _Colin Barker_, Oct 16 2015
%t Select[ Range[ 3000 ], PowerMod[ #, 14, 225 ]==1& ]
%t LinearRecurrence[{1,0,0,1,-1},{1,26,199,224,226},50] (* _Harvey P. Dale_, Nov 11 2011 *)
%o (PARI) a(n) = (-225 - 125*(-1)^n + (171-171*I)*(-I)^n + (171+171*I)*I^n + 450*n)/8 \\ _Colin Barker_, Oct 16 2015
%o (PARI) Vec(x*(1+25*x+173*x^2+25*x^3+x^4)/((1+x)*(1+x^2)*(x-1)^2) + O(x^100)) \\ _Colin Barker_, Oct 16 2015
%Y Cf. A056021, A056022, A056024, A056025, A056027, A056028, A056031, A056034, A056035.
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Jun 08 2000
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