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Numbers k such that the sum of the digits of Fibonacci(k) in base 11 is k.
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%I #47 Sep 08 2022 08:44:49

%S 0,1,5,13,41,53,55,60,61,90,97,169,185,193,215,265,269,353,355,385,

%T 397,437,481,493,617,629,630,653,713,750,769,780,889,905,960,1013,

%U 1025,1045,1205,1320,1405,1435,1501,1620,1650,1657,1705,1735,1769,1793,1913,1981

%N Numbers k such that the sum of the digits of Fibonacci(k) in base 11 is k.

%C In his article, Terr estimated the number of terms to be 684 +- 26, which agrees with the found count of 710. - _Sven Simon_, Aug 06 2006

%H Sven Simon, <a href="/A025490/b025490.txt">Table of n, a(n) for n = 1..711</a> [May be complete]

%H David Terr, <a href="http://www.fq.math.ca/Scanned/34-4/terr.pdf">On the Sums of Digits of Fibonacci Numbers,</a> Fibonacci Quarterly 34, Aug. 1996, pp. 349-355.

%o (PARI) isok(n) = sumdigits(fibonacci(n), 11) == n; \\ _Michel Marcus_, Jun 08 2019

%o (Magma) [k:k in [0..2000]| &+Intseq(Fibonacci(k),11) eq k]; // _Marius A. Burtea_, Jun 09 2019

%Y Cf. A020995 (base 10), A020996 (base 12).

%Y Cf. A025491 (with Lucas numbers).

%K base,nonn

%O 1,3

%A _David W. Wilson_

%E Title clarified and offset changed to 1 by _Sean A. Irvine_, May 06 2019