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Search: id:A084799
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| A084799 |
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Least positive integers, all distinct, that satisfy sum(n>0,1/a(n)^z)=0, where z=(3+I*4)/5. |
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13
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| 1, 9, 12, 16, 19, 24, 28, 34, 39, 45, 51, 57, 64, 71, 78, 85, 93, 102, 110, 119, 127, 137, 146, 156, 166, 176, 187, 197, 208, 219, 231, 243, 254, 267, 279, 291, 304, 317, 330, 344, 358, 371, 386, 400, 414, 429, 444, 459, 474, 490, 506, 522, 538, 554, 570, 587
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sequence satisfies sum(n>0,1/a(n)^z)=0 by requiring that the modulus of the successive partial sums are monotonically decreasing in magnitude for the given z.
Sequences A084799 - A084804 are related to zeros of the Riemann zeta function. The least integers that satisfy sum(n>0, 1/a(n)^z ) = 0, where a(1)=1, a(n+1)>a(n), and z = unit complex numbers using Pythagorean triples: (3+I*4)/5, (4+I*3)/5, (12+I*5)/13, (24+I*7)/25, (40+I*9)/41; these z produce a special pattern to the sequences.
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PROGRAM
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(PARI) S=0; w=1; a=0; for(n=1, 100, b=a+1; while(abs(S+exp(-z*log(b)))>w, b++); S=S+exp(-z*log(b)); w=abs(S); a=b; print1(b, ", "))
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CROSSREFS
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Cf. A084588-A084593, A084800-A084810.
Sequence in context: A120167 A048699 A019468 this_sequence A120154 A084375 A076674
Adjacent sequences: A084796 A084797 A084798 this_sequence A084800 A084801 A084802
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 04 2003
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