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A100476
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a(1)=a(2)=a(3)=a(4)=1; for n > 4: a(n) = A000720(a(n-1)+a(n-2)+a(n-3)+a(n-4)).
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| 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 behaviour?
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EXAMPLE
| a(6) = A000720(a(2)+a(3)+a(4)+a(5)) = A000720(5) = 3.
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MATHEMATICA
| 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}] (* From Harvey P. Dale, Sep 19 2011 *)
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CROSSREFS
| Cf. A000078, A000720.
Sequence in context: A076332 A092601 A162906 * A007896 A074139 A017832
Adjacent sequences: A100473 A100474 A100475 * A100477 A100478 A100479
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 22 2004
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EXTENSIONS
| Edited by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Aug 08 2007
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