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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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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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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LINKS
| Paul D. Hanna, Table of n, a(n) for n = 1..500
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FORMULA
| 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.
The constant S = Sum_{n>=1} 1/a(n) is more precisely given by:
S = 1.7767914254 8765842099 7295125934 3751657100 4017014991 1002131974 4535225732 9321570657 9706460392 2109445017 4890160620 5702665489 ... (cf. A195202).
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EXAMPLE
| 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
| Cf. A195202 (constant).
Sequence in context: A078140 A143373 A102475 * A114322 A000213 A074858
Adjacent sequences: A066170 A066171 A066172 * A066174 A066175 A066176
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 14 2001
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