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 A111366 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. 0
 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; text; internal format)
 OFFSET 1,2 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? LINKS 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. MATHEMATICA \$MaxExtraPrecision = 10^9; fQ[n_] := Plus @@ IntegerDigits@Floor@(GoldenRatio^n) == Plus @@ IntegerDigits@Fibonacci@n; Select[ Range[6108], fQ[ # ] &] (* Robert G. Wilson v *) CROSSREFS Cf. A066212, A001999. Sequence in context: A064521 A330283 A262238 * A177127 A177175 A301605 Adjacent sequences:  A111363 A111364 A111365 * A111367 A111368 A111369 KEYWORD base,nonn AUTHOR Stefan Steinerberger, Nov 07 2005 EXTENSIONS Edited, corrected and extended by Robert G. Wilson v, Nov 16 2005 STATUS approved

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Last modified January 26 06:41 EST 2022. Contains 350572 sequences. (Running on oeis4.)