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.

A337448 The numbers k for which Fibonacci(k) are Niven numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 12, 18, 36, 54, 72, 84, 112, 120, 144, 160, 180, 198, 200, 216, 240, 243, 264, 286, 288, 299, 324, 358, 360, 468, 504, 528, 540, 576, 648, 720, 780, 816, 1008, 1020, 1044, 1200, 1248, 1260, 1500, 1602, 1824, 1872, 1917, 2160, 2184, 2760
Offset: 1

Views

Author

Marius A. Burtea, Sep 14 2020

Keywords

Comments

For a(7) = 8, Fibonacci(8) = 21 and 21/digsum(21) = 7 is a prime number, so Fibonacci(8) is a Moran number (A001101). It seems that this is the only Moran number among the first 100000 Fibonacci numbers.

Examples

			Fibonacci(1) = 1 = A005349(1), so 1 is a term.
Fibonacci(8) = 21 = A005349(14), so 8 is a term.
Fibonacci(12) = 144 = A005349(8), so 12 is a term.
Fibonacci(18) = 2584 = A005349(514), so 18 is a term.

Links

Crossrefs

Cf. A000045, A004090, A001101, A005349, A117774, A337449.

Programs

  • Magma
    niven:=func; [k:k in [1..2760]| niven(Fibonacci(k))];
  • Mathematica
    nivenQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; Select[Range[3000], nivenQ[Fibonacci[#]] &] (* Amiram Eldar, Sep 15 2020 *)
  • PARI
    isok(k) = my(f=fibonacci(k)); (f % sumdigits(f)) == 0; \\ Michel Marcus, Sep 15 2020

A117725 Zeroless numbers for which the sum of the digits and the product of the digits are both Fibonacci numbers.

Original entry on oeis.org

1, 2, 3, 5, 8, 11, 12, 21, 111, 113, 131, 311, 1112, 1115, 1121, 1124, 1142, 1151, 1211, 1214, 1241, 1412, 1421, 1511, 2111, 2114, 2141, 2411, 4112, 4121, 4211, 5111, 11111, 11137, 11173, 11222, 11289, 11298, 11317, 11371, 11713, 11731, 11829, 11892, 11928
Offset: 1

Views

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006

Keywords

Examples

			18192 is a term because the sum of its digits is 1+8+1+9+2 = 21, the product of its digits is 1*8*1*9*2 = 144 and both 21 and 144 are Fibonacci numbers.

Links

Crossrefs

Cf. A000045, A117774.
Subsequence of A028840, A028890 and of A052382.

Programs

  • Mathematica
    isFibonacci[x_]:=MemberQ[Array[Fibonacci,2x],x];DeleteCases[ParallelTable[If[And[isFibonacci[Times@@IntegerDigits[n]],isFibonacci[Total[IntegerDigits[n]]]],n,a],{n,1,15000}],a] (* J.W.L. (Jan) Eerland, Jan 03 2024 *)
  • PARI
    isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || issquare(k-8); \\ A000045
isok(k) = my(d=digits(k)); vecmin(d) && isfib(vecsum(d)) && isfib(vecprod(d)); \\ Michel Marcus, Jan 03 2024
  • PARI
    \\ See PARI program in links

Extensions

a(45) from J.W.L. (Jan) Eerland, Jan 03 2024
Name clarified by Michel Marcus, Jan 03 2024

A353988 Numbers k such that Fibonacci(k) is a binary Niven number (A049445).

Original entry on oeis.org

1, 2, 3, 6, 8, 9, 10, 12, 18, 24, 30, 36, 48, 56, 60, 100, 120, 144, 150, 168, 240, 270, 288, 300, 324, 330, 336, 360, 444, 540, 594, 600, 624, 720, 750, 840, 864, 896, 900, 936, 1080, 1152, 1200, 1210, 1360, 1404, 1632, 1720, 1921, 2028, 2400, 2520, 2552, 2864
Offset: 1

Views

Author

Amiram Eldar, May 13 2022

Keywords

Comments

Numbers k such that A011373(k) | A000045(k).

Examples

			1 is a term since A000045(1) = A011373(1) = 1 and 1 | 1.
10 is a term since A000045(10) = 55, A011373(1) = 5 and 5 | 55.

Links

Crossrefs

Cf. A000045, A000120, A011373, A049445, A117774, A337448 (decimal analog).

Programs

  • Mathematica
    Select[Range[3000], Divisible[(f = Fibonacci[#]), DigitCount[f, 2, 1]] &]
  • PARI
    isok(k) = my(f=fibonacci(k)); ! (f % hammingweight(f)); \\ Michel Marcus, May 13 2022
Showing 1-3 of 3 results.

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

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