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A006133 Related to representations as sums of Fibonacci numbers.

%I A006133 M3080 #22 Jul 08 2025 16:41:35
%S A006133 3,21,32,79,144,155,173,202,220,231,401,524,542,553,600,922,987,998,
%T A006133 1016,1045,1063,1074,1121,1139,1150,1168,1186,1197,1215,1244,1367,
%U A006133 1385,1396,1443,1508,1519,1537,1566,1584,1595,1765,2608,2731,2749,2760,2807,3129
%N A006133 Related to representations as sums of Fibonacci numbers.
%C A006133 Common value of A003231(x) and A003234(x) for x in A006132 (see Table 1 p. 357 in Carlitz link). - _Michel Marcus_, Feb 02 2014
%D A006133 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006133 L. Carlitz, R. Scoville and T. Vaughan, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/11-4/carlitz.pdf">Some arithmetic functions related to Fibonacci numbers</a>, Fib. Quart., 11 (1973), 337-386.
%F A006133 a(n) = A003231(A006132(n)) = A003234(A006132(n)). - _Michel Marcus_, Feb 02 2014
%o A006133 (PARI) A001950(n) = floor(n*(sqrt(5)+3)/2); \\ b
%o A006133 A003231(n) = floor(n*(sqrt(5)+5)/2); \\ c
%o A006133 iss(n) = A003231(A001950(n)) == A001950(A003231(n)) - 1;
%o A006133 lista(nn) = {v003231 = vector(nn, i, floor(i*(sqrt(5)+5)/2)); v003234 = select(n->iss(n), vector(5*nn, i, i)); for (n=1, nn, if (v003231[n] == v003234[n], print1(v003231[n], ", ")););}  \\ _Michel Marcus_, Feb 02 2014
%K A006133 nonn
%O A006133 1,1
%A A006133 _N. J. A. Sloane_
%E A006133 More terms from _Michel Marcus_, Feb 02 2014