A080457 a(1)=3; for n>1, a(n)=a(n-1) if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

3, 7, 7, 11, 15, 19, 19, 23, 27, 31, 31, 35, 39, 43, 43, 47, 51, 55, 55, 59, 63, 67, 67, 71, 75, 79, 79, 83, 87, 91, 91, 95, 99, 103, 103, 107, 111, 115, 115, 119, 123, 127, 127, 131, 135, 139, 139, 143, 147, 151, 151, 155, 159, 163, 163, 167, 171, 175

Offset: 1

Author

N. J. A. Sloane and Benoit Cloitre, Mar 20 2003

Keywords

• nonn
• easy

Links

• B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
• B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A080036, A080037, A080455, A080456, A080457, A080458.

Programs

Magma

[3+4*(n-2-Floor((n-3)/4)) : n in [1..100]]; // Wesley Ivan Hurt, Jul 15 2015

Maple

A080457:=n->3+4*(n-2-floor((n-3)/4)): seq(A080457(n), n=1..100); # Wesley Ivan Hurt, Jul 15 2015

Mathematica

CoefficientList[Series[(3 + 4 x + 4 x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Jul 15 2015 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {3, 7, 7, 11, 15}, 70] (* Vincenzo Librandi, Jul 16 2015 *)

PARI

main(size)={my(v=vector(size),i,j);v[1]=3;for(j=2,size,x=0;for(i=1,j-1,if(v[i]==j,x=1;break));if(x==1,v[j]=v[j-1],v[j]=v[j-1]+4));return(v);} /* Anders Hellström, Jul 15 2015 */

Formula

a(n) = 3 + 4*(n-2-floor((n-3)/4)).

From Wesley Ivan Hurt, Jul 15 2015: (Start)

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

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

a(n) = (6*n-1+(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/2. (End)