A047610 Positive integers that are congruent to {1, 4, 5} mod 8.

1, 4, 5, 9, 12, 13, 17, 20, 21, 25, 28, 29, 33, 36, 37, 41, 44, 45, 49, 52, 53, 57, 60, 61, 65, 68, 69, 73, 76, 77, 81, 84, 85, 89, 92, 93, 97, 100, 101, 105, 108, 109, 113, 116, 117, 121, 124, 125, 129, 132, 133, 137, 140, 141, 145, 148, 149, 153, 156, 157

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..9999

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

Formula

a(n) = a(n-3) + 8, n > 3, with initial conditions a(1) = 1, a(2) = 4, a(3) = 5. - L. Edson Jeffery, May 04 2015

G.f.: x*(1+3*x)*(1+x^2)/(1-x-x^3+x^4). - Robert Israel, May 04 2015

A047610 = A016813 union A017113\{0}. - L. Edson Jeffery, May 06 2015

Maple

seq(op([8*i+1, 8*i+4, 8*i+5]), i=0..100); # Robert Israel, May 04 2015

Mathematica

a[1] := 1; a[2] := 4; a[3] := 5; a[n_] := a[n - 3] + 8; Table[a[n], {n, 10}] (* L. Edson Jeffery, May 04 2015 *)
Select[Range[0, 200], MemberQ[{1, 4, 5}, Mod[#, 8]] &] (* Vincenzo Librandi, May 07 2015 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 4, 5, 9}, 60] (* Harvey P. Dale, Nov 21 2015 *)

Prog

(PARI) is(n)=n%8==1||n%8>>1==2 \\ Charles R Greathouse IV, May 04 2015
(Magma) [n : n in [0..160] | n mod 8 in [1, 4, 5]]; // Vincenzo Librandi, May 07 2015

Crossrefs

Cf. A016813, A017113.

Sequence in context: A194154 A297291 A269741 * A126004 A258251 A331086

Adjacent sequences: A047607 A047608 A047609 * A047611 A047612 A047613

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved