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A100476
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a(n) = A000720(Sum_{j=1..4} a(n-j)) with a(1)=a(2)=a(3)=a(4)=1.
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1
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1, 1, 1, 1, 2, 3, 4, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 18, 18, 19, 20, 21, 21, 22, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24
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OFFSET
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1,5
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COMMENTS
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For n > 29 we have a(n) = 24. Starting with other values of a(1), a(2), a(3), a(4) what behaviors are possible? The sequence is in any case bounded. If for some k a(k) + a(k+1) + a(k+2) + a(k+3) > 400, then a(k+4) is smaller than the average of a(k), a(k+1), a(k+2) and a(k+3), which means that the sequence will always stick at a single integer after some point or go into a loop. Are there values a(1), a(2), a(3), a(4) such that the sequence would indeed exhibit cyclic behavior?
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LINKS
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EXAMPLE
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MATHEMATICA
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a={1, 1, 1, 1}; Do[ AppendTo[a, PrimePi[a[[-1]]+a[[-2]]+a[[-3]]+a[[-4]]]], {70}]; a
RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==PrimePi[a[n-1]+ a[n-2]+ a[n-3]+a[n-4]]}, a[n], {n, 80}] (* Harvey P. Dale, Sep 19 2011 *)
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PROG
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(SageMath)
@CachedFunction
if (n<5): return 1
else: return prime_pi( sum(a(n-j) for j in range(1, 5)) )
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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