cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A020995 Numbers k such that the sum of the digits of Fibonacci(k) is k.

Original entry on oeis.org

0, 1, 5, 10, 31, 35, 62, 72, 175, 180, 216, 251, 252, 360, 494, 504, 540, 946, 1188, 2222
Offset: 1

Views

Author

Sven Simon

Keywords

Comments

Since the number of digits in the k-th Fibonacci number ~ k*log_10(Golden Ratio), theoretically this sequence is infinite, but then the average density of those digits = ~ 0.208987. - Robert G. Wilson v
Robert Dawson of Saint Mary's University says it is likely that 2222 is the last term, as (assuming that the digits are equally distributed) the expected digit sum is ~ 0.9*k. - Stefan Steinerberger, Mar 12 2006 [Assuming that the average digit is (0+1+2+...+9)/10 = 9/2, the expected digit sum is ~ (9/2)*log_10((1+sqrt(5))/2)*k = 0.94044438...*k. - Jon E. Schoenfield, Aug 28 2022]
Bankoff's short paper lists the first seven terms. - T. D. Noe, Mar 19 2012
No more terms < 150000. - Manfred Scheucher, Aug 03 2015
If it exists, a(21) > 10^6. - Robert Price, May 26 2019

Examples

			Fibonacci(10) = 55 and 5+5 = 10.

References

  • Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, Prometheus Books, NY, 2007, page 209.

Links

Crossrefs

Cf. A000045, A067515, A004090.

Programs

  • Mathematica
    Do[ If[ Apply[ Plus, IntegerDigits[ Fibonacci[n]]] == n, Print[n]], {n, 1, 10^5} ] (* Sven Simon *)
Do[ If[ Mod[ Fibonacci[n], 9] == Mod[n, 9], If[ Plus @@ IntegerDigits[ Fibonacci[n]] == n, Print[n]]], {n, 0, 10^6}] (* Robert G. Wilson v *)
Select[Range[0, 10^5], Plus @@ IntegerDigits[Fibonacci[ # ]] == # &] (* Ron Knott, Oct 30 2010 *)
  • PARI
    isok(n) = sumdigits(fibonacci(n)) == n; \\ Michel Marcus, Feb 18 2015

A111331 Prime Fibonacci numbers whose digits in base 10 sum up to a prime.

Original entry on oeis.org

2, 3, 5, 89, 514229, 433494437, 2971215073, 3061719992484545030554313848083717208111285432353738497131674799321571238149015933442805665949
Offset: 1

Views

Author

Stefan Steinerberger, Nov 05 2005

Keywords

Comments

Fibonacci(104911) is the next (probable) prime whose digits sum to a prime. Thus the next term would be 21925 digits long. - Hans Havermann, Nov 06 2005

Examples

			514229 is a prime Fibonacci number and the sum of the digits 5 + 1 + 4 + 2 + 2 + 9 = 23 is also a prime.

Crossrefs

Cf. A065398, A051694, A051694, A067515.

Programs

  • Mathematica
    Select[Fibonacci[Range[1000]],PrimeQ[#]&&PrimeQ[Total[IntegerDigits[#]]]&] (* James C. McMahon, May 31 2024 *)

A383045 Integers k for which the sum of digits of Fibonacci(k) is a Fibonacci number.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 13, 28, 33, 49, 85, 94, 107, 286, 299, 366, 421, 422, 443, 657, 2807, 4483, 4531, 18694, 49140, 79033, 79850, 80290, 128306, 129049, 129618, 208245, 338888, 546571, 882766, 883822, 886342
Offset: 1

Views

Author

Michel Marcus, Apr 14 2025

Keywords

Examples

			Fibonacci(8) = 21 and sumdigits(21) = 3, a Fibonacci number, so 8 is a term.

Crossrefs

Cf. A000045, A020995, A067515, A004090, A178837, A382053.

Programs

  • Maple
    q:= n-> (t-> issqr(t+4) or issqr(t-4))(5*add(i, i=convert(combinat[fibonacci](n), base, 10))^2):
select(q, [$0..4600])[];  # Alois P. Heinz, Jul 15 2025
  • Mathematica
    fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}]; Select[Range[0, 1000], fibQ[DigitSum[Fibonacci[#]]] &] (* Amiram Eldar, Apr 14 2025 *)
  • PARI
    isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(k) = isfib(sumdigits(fibonacci(k)));

Extensions

a(36)-a(39) from Amiram Eldar, Apr 14 2025
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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