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Search: id:A059534
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| A059534 |
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Beatty sequence for 1+1/Catalan's constant. |
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+0
3
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| 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni, Michael; Characterization of the set of values f(n)=[n alpha], n=1,2,... Discrete Math.2 (1972), no.4,335-345.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,2000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Beatty sequences
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PROGRAM
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(PARI) { digits=100; default(realprecision, digits+80); s=1.0; n=5*digits; j=4*n+1; si=-1.0; for (i=3, j-2, s+=si/i^2; si=-si; i++; ); s+=0.5/j^2; ttk=4.0; d=4.0*j^3; xk=2.0; xkp=xk; for (k=2, 100000000, term=(ttk-1)*ttk*xkp; xk++; xkp*=xk; if (k>2, term*=xk; xk++; xkp*=xk; ); term*=bernreal(k)/d; sn=s+term; if (sn==s, break); s=sn; ttk*=4.0; d*=(k+1)*(k+2)*j^2; k++; ); b=1 + 1/s; for (n = 1, 2000, write("b059534.txt", n, " ", floor(n*b)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 27 2009]
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CROSSREFS
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Beatty complement is A059533.
Sequence in context: A084563 A064676 A147819 this_sequence A137804 A054965 A059548
Adjacent sequences: A059531 A059532 A059533 this_sequence A059535 A059536 A059537
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KEYWORD
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nonn,easy
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AUTHOR
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Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu), Jan 22, 2001
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