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Search: id:A023532
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| A023532 |
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a(n) = 0 if n of form m(m+3)/2, otherwise 1. |
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53
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| 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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From Stark: "alpha = 0.101101110111101111101111110 ... is irrational. For if alpha were rational, its decimal expansion would be periodic and have a period of length r starting with the k-th digit of the expansion.
"But by the very nature of alpha, there will be blocks of r digits, all 1, in this expansion after the k-th digit and the periodicity would then guarantee that everything after such a block of r digits would also be all ones.
"This contradicts the fact that there will always be zeros occurring after any given point in the expansion of alpha. Hence alpha is irrational."
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REFERENCES
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Harold M. Stark, An Introduction to Number Theory, The MIT Press, Cambridge, Mass, eighth printing 1994, page 170.
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FORMULA
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Blocks of lengths 1, 2, 3, 4, ... ones separated by a single zero.
a(n)=mod(floor(((10^(n+2)-10)/9)10^(n+1-binomial(floor((1+sqrt(9+8n))/2), 2)- (1+floor(log((10^(n+2)-10)/9, 10))))), 10) - Paul Barry (pbarry(AT)wit.ie), May 25 2004
a(n)=1-floor((sqrt(9+8n)-1)/2)+floor((sqrt(1+8n)-1)/2). - Paul Barry (pbarry(AT)wit.ie), May 25 2004
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MATHEMATICA
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a = {}; Do[a = Append[a, Join[ {0}, Table[1, {n} ] ] ], {n, 1, 13} ]; a = Flatten[a]
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CROSSREFS
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Adjacent sequences: A023529 A023530 A023531 this_sequence A023533 A023534 A023535
Sequence in context: A096270 A123640 A022924 this_sequence A112690 A115971 A072165
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 06 2000
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