A020996 - OEIS

%I #33 Jan 05 2025 19:51:34

%S 0,1,5,13,14,89,96,123,221,387,419,550,648,749,866,892,1105,2037

%N Numbers k such that the sum of the digits of Fibonacci(k) in base 12 is k.

%C No more terms < 100000. - _Manfred Scheucher_, Aug 03 2015

%H Manfred Scheucher, <a href="/A020996/a020996.sage.txt">Sage Script</a>

%H David Terr, <a href="https://web.archive.org/web/2024*/https://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.

%p filter:= proc(n) convert(convert(combinat:-fibonacci(n),base,12),`+`)=n end proc:

%p select(filter, [$1..3000]); # _Robert Israel_, Aug 03 2015

%o (PARI) isok(n) = vecsum(digits(fibonacci(n), 12)) == n; \\ _Michel Marcus_, Feb 18 2015

%Y Cf. A020995 (base 10), A025490 (base 11).

%K nonn,base,more

%O 1,3

%A _Sven Simon_

%E a(1)=0 inserted by _Sean A. Irvine_, May 06 2019