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A111366
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Numbers such that the sum of the digits of floor(phi^n) is also the sum of the digits of the n-th Fibonacci number (in base 10), where phi is the golden ratio.
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0
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1, 6, 13, 61, 73, 92, 97, 198, 212, 217, 222, 270, 349, 380, 404, 438, 524, 630, 649, 836, 937, 1446, 1477, 1513, 1532, 1729, 2005, 2046, 2060, 2077, 2209, 2348, 2660, 2862, 2934, 3265, 3649, 3889, 4093, 4609, 4686, 4945, 5180, 5444, 5497, 5749, 5929, 6102
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Questions: (1) Is this sequence infinite? (2) Are the gaps between the elements of this sequence bounded from above? (3) If this sequence is infinite, what is its asymptotic growth? (4) Consider the definition of this sequence for other values c instead of the golden ratio. What are the properties of this modified sequence?
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EXAMPLE
| trunc(phi^6) = 17, the 6th Fibonacci number is 8; the sum of their digits is the same, thus 6 is in the sequence.
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MATHEMATICA
| $MaxExtraPrecision = 10^9; fQ[n_] := Plus @@ IntegerDigits@Floor@(GoldenRatio^n) == Plus @@ IntegerDigits@Fibonacci@n; Select[ Range[6108], fQ[ # ] &] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A066212, A001999.
Sequence in context: A003757 A187985 A064521 * A177127 A177175 A119110
Adjacent sequences: A111363 A111364 A111365 * A111367 A111368 A111369
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KEYWORD
| base,nonn
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AUTHOR
| Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 07 2005
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EXTENSIONS
| Edited, corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Nov 16 2005
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