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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A016813, A017113.

Programs

Magma

[n : n in [0..160] | n mod 8 in [1,4,5]]; // Vincenzo Librandi, May 07 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 *)

PARI

is(n)=n%8==1||n%8>>1==2 \\ Charles R Greathouse IV, May 04 2015

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