A056082 Numbers k such that k^4 == 1 (mod 5^3).

1, 57, 68, 124, 126, 182, 193, 249, 251, 307, 318, 374, 376, 432, 443, 499, 501, 557, 568, 624, 626, 682, 693, 749, 751, 807, 818, 874, 876, 932, 943, 999, 1001, 1057, 1068, 1124, 1126, 1182, 1193, 1249, 1251, 1307, 1318, 1374, 1376, 1432, 1443, 1499, 1501

Offset

1,2

Comments

Numbers that are congruent to {1, 57, 68, 124} mod 125.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Formula

From Wesley Ivan Hurt, Jun 07 2016: (Start)

G.f.: x*(1+56*x+11*x^2+56*x^3+x^4)/((x-1)^2*(1+x+x^2+x^3)).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (250*n-125+99*i^(2*n)+(9-9*i)*i^(-n)+(9+9*i)*i^n)/8 where i=sqrt(-1). (End)

Maple

A056082:=n->(250*n-125+99*I^(2*n)+(9-9*I)*I^(-n)+(9+9*I)*I^n)/8: seq(A056082(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

x=5; Select[ Range[ 1000 ], PowerMod[ #, x-1, x^3 ]==1& ]

Prog

(Magma) [n : n in [0..2000] | n mod 125 in [1, 57, 68, 124]]; // Wesley Ivan Hurt, Jun 07 2016

Crossrefs

Cf. A056083, A056084, A056085, A056086, A056087, A056088, A056089.

Sequence in context: A216183 A334238 A336328 * A218562 A067809 A176636

Adjacent sequences: A056079 A056080 A056081 * A056083 A056084 A056085

Keyword

nonn,easy

Author

Robert G. Wilson v, Jun 08 2000

Status

approved