This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111366 #5 Oct 31 2013 12:17:32 %S A111366 1,6,13,61,73,92,97,198,212,217,222,270,349,380,404,438,524,630,649, %T A111366 836,937,1446,1477,1513,1532,1729,2005,2046,2060,2077,2209,2348,2660, %U A111366 2862,2934,3265,3649,3889,4093,4609,4686,4945,5180,5444,5497,5749,5929,6102 %N 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. %C A111366 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? %e A111366 trunc(phi^6) = 17, the 6th Fibonacci number is 8; the sum of their digits is the same, thus 6 is in the sequence. %t A111366 $MaxExtraPrecision = 10^9; fQ[n_] := Plus @@ IntegerDigits@Floor@(GoldenRatio^n) == Plus @@ IntegerDigits@Fibonacci@n; Select[ Range[6108], fQ[ # ] &] (* _Robert G. Wilson v_ *) %Y A111366 Cf. A066212, A001999. %K A111366 base,nonn %O A111366 1,2 %A A111366 _Stefan Steinerberger_, Nov 07 2005 %E A111366 Edited, corrected and extended by _Robert G. Wilson v_, Nov 16 2005