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Search: id:A066173
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| A066173 |
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Self-reciprocating sequence: the integer part of powers of the reciprocal sum. |
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+0
1
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| 1, 3, 5, 9, 17, 31, 55, 99, 176, 313, 557, 990, 1759, 3125, 5553, 9866, 17531, 31149, 55346, 98339, 174729, 310457, 551617, 980109, 1741450, 3094195, 5497739, 9768336, 17356295, 30838517, 54793613, 97356822, 172982767, 307354297
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence and its reciprocal sum are unique: there exists only one self-reciprocating sequence whose terms are exactly equal to the integer part of the powers of the sum of the reciprocal terms of the same sequence.
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FORMULA
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a(n) = floor[S^n], where S=1.776791425488... = Sum 1/a(k), k=1, 2, 3, ... The n-th term of the sequence is the integer part of the n-th power of the sum of the infinite series of reciprocal terms of this same sequence.
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EXAMPLE
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1=[S], 3=[S^2], 5=[S^3], 9=[S^4], 17=[S^5], 31=[S^6], 55=[S^7], ... where S=1/1 + 1/3 + 1/5 + 1/9 + 1/17 + 1/31 + 1/55 + 1/99 + 1/176 +...
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CROSSREFS
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Adjacent sequences: A066170 A066171 A066172 this_sequence A066174 A066175 A066176
Sequence in context: A077879 A078140 A102475 this_sequence A114322 A000213 A074858
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 14 2001
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