A080033 a(n) is taken to be the smallest positive integer not already present which is consistent with the condition "n is a member of the sequence if and only if a(n) is a multiple of 4".
0, 2, 4, 5, 8, 12, 7, 16, 20, 10, 24, 13, 28, 32, 15, 36, 40, 18, 44, 21, 48, 52, 23, 56, 60, 26, 64, 29, 68, 72, 31, 76, 80, 34, 84, 37, 88, 92, 39, 96, 100, 42, 104, 45, 108, 112, 47, 116, 120, 50, 124, 53, 128, 132, 55, 136, 140, 58, 144, 61, 148, 152, 63, 156, 160, 66
Offset: 0
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)
Formula
a(8m)=20m, a(8m+1)=8m+2, a(8m+2)=20m+4, a(8m+3)=8m+5, a(8m+4)=20m+8, a(8m+5)=20m+12, a(8m+6)=8m+7, a(8m+7)=20m+16.
From Chai Wah Wu, Sep 27 2016: (Start)
a(n) = 2*a(n-8) - a(n-16) for n > 15.
G.f.: x*(4*x^14 + x^13 + 8*x^12 + 12*x^11 + 3*x^10 + 16*x^9 + 6*x^8 + 20*x^7 + 16*x^6 + 7*x^5 + 12*x^4 + 8*x^3 + 5*x^2 + 4*x + 2)/(x^16 - 2*x^8 + 1). (End)
Extensions
More terms from Matthew Vandermast, Mar 23 2003