A130048 Complement of inductive sum sequence A130049.
1, 2, 4, 5, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85
Offset: 1
Keywords
Examples
(a(1),a(2),...,a(6))=(1,2,4,5,8,9), so x=4 and b(6)=1+2+4+5=12. (a(1),a(2),...,a(7))=(1,2,4,5,8,9,10), so y=4 and b(7)=5+8+9+10=32.
Formula
a(1)=1, a(2)=2, b(1)=0, b(2)=3; for n>=3, let x=Floor(n/2) and y=n-x+1. Then a(n)=least positive integer not among a(1),a(2),...,a(n-1), b(1),b(2),...b(n-1) and b(n)=a(1)+a(2)+...+a(x) if n is even, b(n)=a(y)+a(y+1)+...+a(n) if n is odd.
Comments