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Search: id:A088663
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| A088663 |
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An alternating self-similar sequence of a Sierpinski type with an infinite Pisot root scale. |
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1
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| 0, 0, -1, 0, 1, 0, -8, 0, 25, 0, -97, 0, 367, 0, -1398, 0, 5259, 0, -19878, 0, 75319, 0, -285137, 0, 1078711, 0, -4081933, 0, 15449144, 0, -58467488, 0, 221260378, 0, -837337471, 0, 3168858565, 0, -11992319160, 0, 45383925816, 0, -171751869342, 0, 649981903584, 0, -2459806349188, 0
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Since both 1/n! and (E/(2-E))^n terms can be used to get E, I have mapped the infinite Pisot roots to a self-similar subtractive function like that I used for the factorial.
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FORMULA
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p[n_, k_]=Product[(E/(2-E))^i, {i, 1, n}]/Product[(E/(2-E))^i, {i, Floor[n/2^k], n}] a(n) = Sum[Floor[p[n, k]/(8*p[n-1, k])], {k, 1, 8}]
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MATHEMATICA
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p[n_, k_]=Product[(E/(2-E))^i, {i, 1, n}]/Product[(E/(2-E))^i, {i, Floor[n/2^k], n}] digits=80 f[n_]=Sum[Floor[p[n, k]/(8*p[n-1, k])], {k, 1, 8}] at=Table[f[n], {n, 2, digits}]
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CROSSREFS
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Cf. A088487 A self similar Sierpinski type chaotic sequence with rate three at eight levels. A088488 A self similar Cantor type sequence with eight levels.
Sequence in context: A167300 A167347 A028604 this_sequence A011997 A047771 A137528
Adjacent sequences: A088660 A088661 A088662 this_sequence A088664 A088665 A088666
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 21 2003
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