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.

A028890 Product of digits of n is a nonzero Fibonacci number.

Original entry on oeis.org

1, 2, 3, 5, 8, 11, 12, 13, 15, 18, 21, 24, 31, 37, 42, 51, 73, 81, 111, 112, 113, 115, 118, 121, 124, 131, 137, 142, 151, 173, 181, 211, 214, 222, 241, 289, 298, 311, 317, 368, 371, 386, 412, 421, 449, 466, 494, 511, 638, 646, 664, 683, 713, 731, 811, 829, 836
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Numbers n whose product of digits is 1, 2, 3, 5, 8, 21, or 144 (these being the only 7-smooth Fibonacci numbers). - Robert Israel, Jan 26 2020

Links

Crossrefs

Cf. A007954, A028891, A028840.

Programs

  • Maple
    select(t -> member(convert(convert(t,base,10),`*`),[1, 2, 3, 5, 8, 21, 144]),[$1..999]); # Robert Israel, Jan 26 2020

Extensions

More terms from Erich Friedman.
Name clarified and offset changed by Robert Israel, Jan 26 2020

A028841 Iterated sum of digits of n is a Fibonacci number.

Original entry on oeis.org

1, 2, 3, 5, 8, 10, 11, 12, 14, 17, 19, 20, 21, 23, 26, 28, 29, 30, 32, 35, 37, 38, 39, 41, 44, 46, 47, 48, 50, 53, 55, 56, 57, 59, 62, 64, 65, 66, 68, 71, 73, 74, 75, 77, 80, 82, 83, 84, 86, 89, 91, 92, 93, 95, 98, 100, 101, 102, 104, 107, 109, 110, 111, 113, 116, 118, 119
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Intermediate iterations don't count. For example, with 85, we have 8 + 5 = 13, which is a Fibonacci number, but 1 + 3 = 4, which is not a Fibonacci numbers, so 85 is not in the sequence. - Alonso del Arte, Jan 20 2020

Examples

			98 -> 9 + 8 = 17 -> 1 + 7 = 8 is a Fibonacci number.

Links

Crossrefs

Cf. A010888, A028840, A028891.

Programs

  • Mathematica
    With[{fibo = {1, 2, 3, 5, 8}}, Select[Range[120], MemberQ[fibo, NestWhile[Total[IntegerDigits[#]] &, #, # > 9 &]]&]] (* Harvey P. Dale, Apr 11 2013 *)
  • Scala
    def fiboDRQ(n: Int): Boolean = List(1, 2, 3, 5, 8).contains(n % 9)
(1 to 100).filter(fiboDRQ) // Alonso del Arte, Jan 28 2020

Formula

Conjectures from Colin Barker, Feb 18 2020: (Start)
G.f.: x*(1 + x + x^2 + 2*x^3 + 3*x^4 + x^5) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(n-1) + a(n-5) - a(n-6) for n>6.
(End)

Extensions

More terms from Patrick De Geest, Jun 15 1999
Offset corrected to 1 by Alonso del Arte, Jan 28 2020 at Michel Marcus's suggestion

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
Showing 1-3 of 3 results.

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

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