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A309567
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a(1) = 4, a(2) = 2, a(3) = 5, a(4) = 3, a(5) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-4)) for n > 5.
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5
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4, 2, 5, 3, 1, 4, 7, 5, 8, 6, 4, 12, 5, 13, 6, 9, 17, 5, 18, 6, 9, 22, 5, 23, 11, 9, 27, 5, 28, 11, 9, 32, 5, 33, 11, 14, 37, 5, 38, 11, 14, 42, 5, 43, 11, 14, 47, 5, 48, 16, 14, 52, 5, 53, 16, 14, 57, 5, 58, 16, 14, 62, 5, 63, 16, 19, 67, 5, 68, 16, 19, 72, 5, 73, 16, 19, 77, 5, 78, 16, 19, 82, 5, 83, 21, 19, 87, 5
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OFFSET
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1,1
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COMMENTS
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A well-defined quasi-periodic solution for Hofstadter V recurrence (a(n) = a(n-a(n-1)) + a(n-a(n-4))).
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LINKS
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FORMULA
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For k >= 1:
a(5*k) = 5*floor(sqrt(k-1))+1,
a(5*k+1) = 5*round(sqrt(k))-1,
a(5*k+2) = 5*k+2,
a(5*k+3) = 5,
a(5*k+4) = 5*k+3.
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MAPLE
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f:= proc(n) local k, j;
j:= n mod 5;
k:= (n-j)/5;
if j=0 then 5*floor(sqrt(k-1))+1
elif j=1 then 5*round(sqrt(k))-1
elif j=2 then 5*k+2
elif j=3 then 5
else 5*k+3
fi
end proc:
f(1):= 4:
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MATHEMATICA
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a[n_] := a[n] = If[n < 6, {4, 2, 5, 3, 1}[[n]], a[n - a[n-1]] + a[n - a[n-4]]]; Array[a, 88] (* Giovanni Resta, Aug 08 2019 *)
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PROG
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(PARI) q=vector(100); q[1]=4; q[2]=2; q[3]=5; q[4]=3; q[5]=1; for(n=6, #q, q[n]=q[n-q[n-1]]+q[n-q[n-4]]); q
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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