A037619 Base 5 digits are, in order, the first n terms of the periodic sequence with initial period 2,0,3.

2, 10, 53, 267, 1335, 6678, 33392, 166960, 834803, 4174017, 20870085, 104350428, 521752142, 2608760710, 13043803553, 65219017767, 326095088835, 1630475444178, 8152377220892, 40761886104460, 203809430522303, 1019047152611517

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

• Index entries for 5-automatic sequences.
• Index entries for linear recurrences with constant coefficients, signature (5,0,1,-5).

Programs

Mathematica

nn=30;With[{c=PadRight[{},nn,{2,0,3}]},Table[FromDigits[Take[c,n],5],{n,nn}]] (* Harvey P. Dale, Aug 29 2012 *)

PARI

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -5,1,0,5]^(n-1)*[2;10;53;267])[1,1] \\ Charles R Greathouse IV, Feb 13 2017

Formula

G.f.: x*(2+3*x^2) / ( (x-1)*(5*x-1)*(1+x+x^2) ). - R. J. Mathar, Apr 27 2015

A007091(a(n)) = A037624(n). - R. J. Mathar, Apr 27 2015