A025490 Numbers k such that the sum of the digits of Fibonacci(k) in base 11 is k.

0, 1, 5, 13, 41, 53, 55, 60, 61, 90, 97, 169, 185, 193, 215, 265, 269, 353, 355, 385, 397, 437, 481, 493, 617, 629, 630, 653, 713, 750, 769, 780, 889, 905, 960, 1013, 1025, 1045, 1205, 1320, 1405, 1435, 1501, 1620, 1650, 1657, 1705, 1735, 1769, 1793, 1913, 1981

Offset: 1

Author

David W. Wilson

Keywords

• base
• nonn

Comments

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

Links

• Sven Simon, Table of n, a(n) for n = 1..711 [May be complete]
• David Terr, On the Sums of Digits of Fibonacci Numbers, Fibonacci Quarterly 34, Aug. 1996, pp. 349-355.

Crossrefs

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

Cf. A025491 (with Lucas numbers).

Programs

Magma

[k:k in [0..2000]| &+Intseq(Fibonacci(k),11) eq k]; // Marius A. Burtea, Jun 09 2019

PARI

isok(n) = sumdigits(fibonacci(n), 11) == n; \\ Michel Marcus, Jun 08 2019

Extensions

Title clarified and offset changed to 1 by Sean A. Irvine, May 06 2019