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A056026
Numbers k such that k^14 == 1 (mod 15^2).
10
1, 26, 199, 224, 226, 251, 424, 449, 451, 476, 649, 674, 676, 701, 874, 899, 901, 926, 1099, 1124, 1126, 1151, 1324, 1349, 1351, 1376, 1549, 1574, 1576, 1601, 1774, 1799, 1801, 1826, 1999, 2024, 2026, 2051, 2224, 2249, 2251, 2276, 2449, 2474, 2476, 2501
OFFSET
1,2
COMMENTS
Numbers congruent to {1, 26, 129, 224} mod 225.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Colin Barker)
FORMULA
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
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
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
MATHEMATICA
Select[ Range[ 3000 ], PowerMod[ #, 14, 225 ]==1& ]
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 26, 199, 224, 226}, 50] (* Harvey P. Dale, Nov 11 2011 *)
PROG
(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
(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
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Jun 08 2000
STATUS
approved