A056026 Numbers k such that k^14 == 1 (mod 15^2).

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

Author

Robert G. Wilson v, Jun 08 2000

Keywords

• nonn
• easy

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)
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A056021, A056022, A056024, A056025, A056027, A056028, A056031, A056034, A056035.

Programs

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 *)

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

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