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A248982
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Sequence of distinct least positive numbers such that the average of the first n terms is a Fibonacci number.
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1
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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
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..51.
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FORMULA
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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).
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EXAMPLE
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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.
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PROG
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(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++)
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CROSSREFS
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Sequence in context: A091461 A078091 A073883 * A333446 A289069 A074718
Adjacent sequences: A248979 A248980 A248981 * A248983 A248984 A248985
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KEYWORD
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nonn
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AUTHOR
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Derek Orr, Oct 18 2014
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STATUS
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approved
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