A248982 Sequence of distinct least positive numbers such that the average of the first n terms is a Fibonacci number.

1, 3, 2, 6, 13, 5, 26, 8, 53, 93, 21, 177, 34, 328, 55, 599, 89, 1079, 144, 1924, 233, 3401, 377, 5969, 610, 10412, 987, 18067, 1597, 31207, 2584, 53688, 4181, 92037, 6765, 157281, 10946, 268016, 17711, 455551, 28657, 772519, 46368, 1307276, 75025, 2207953, 121393, 3722593, 196418, 6266068, 317811

Offset

1,2

Links

Table of n, a(n) for n=1..51.

Formula

Conjecture: a(n) = 2*a(n-2)+a(n-4)-2*a(n-6)-a(n-8) for n > 17. - Colin Barker, Oct 19 2014

Empirical g.f.: x*(x -1)*(40*x^15 +98*x^13 +4*x^11 +3*x^10 -80*x^9 +7*x^8 -2*x^6 -2*x^5 -12*x^4 -4*x^3 -4*x^2 -4*x -1) / (x^4 +x^2 -1)^2. - Colin Barker, Oct 19 2014

Conjecture: For n > 4, a(2*n+1) = A000045(n+3).

Example

1/1 = 1 is a Fibonacci number. So a(1) = 1.
(1+2)/2 is not a Fibonacci number. (1+3)/2 = 2 is a Fibonacci number. So a(2) = 3.
(1+3+2)/3 = 2 is a Fibonacci number. So a(3) = 2.

Prog

(PARI) v=[]; n=1; while(n<10^7, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=1, n+2, if(fibonacci(i)>(num/(#v+1)), break); if(fibonacci(i)==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=1; break))); n++)

Crossrefs

Sequence in context: A091461 A078091 A073883 * A333446 A289069 A074718

Adjacent sequences: A248979 A248980 A248981 * A248983 A248984 A248985

Keyword

nonn

Author

Derek Orr, Oct 18 2014

Status

approved