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 1-5 of 5 results.

A004685 Fibonacci numbers written in base 2.

Original entry on oeis.org

0, 1, 1, 10, 11, 101, 1000, 1101, 10101, 100010, 110111, 1011001, 10010000, 11101001, 101111001, 1001100010, 1111011011, 11000111101, 101000011000, 1000001010101, 1101001101101, 10101011000010, 100010100101111, 110111111110001, 1011010100100000, 10010010100010001
Offset: 0

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Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004686 .. A004694: Fibonacci numbers written in base 3, 4, ..., 13.
Cf. A004676 .. A004684: Primes written in base 2, 3, 4, ..., 11.
Cf. A004643, ..., A004668 : powers of 2 resp. of 3 in base 3, 4, 5, ..., 26.

Programs

  • Magma
    [Seqint(Intseq(Fibonacci(n),2)): n in [0..50]]; // G. C. Greubel, Oct 09 2018
  • Maple
    with(combinat): seq(convert(fibonacci(n),binary),n=0..25); # Muniru A Asiru, Oct 10 2018
  • Mathematica
    Table[FromDigits[IntegerDigits[Fibonacci[n], 2]], {n, 0, 30}] (* Stefan Steinerberger, Apr 14 2006 *)
  • PARI
    a(n)=subst(Pol(binary(fibonacci(n))),'x,10) \\ Charles R Greathouse IV, Feb 03 2014
  • PARI
    apply( n->fromdigits(binary(fibonacci(n))), [0..19]) \\ M. F. Hasler, Jun 22 2018
  • PARI
    vector(50, n, n--; fromdigits(digits(fibonacci(n), 2))) \\ G. C. Greubel, Oct 09 2018

Formula

a(n) = A007088(A000045(n)). - Jonathan Vos Post, Aug 24 2010

A004667 Powers of 3 written in base 13. (Next term contains a non-decimal digit.)

Original entry on oeis.org

1, 3, 9, 21, 63, 159, 441
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A000079, A004643, ..., A004655: powers of 2 written in base 10, 4, 5, ..., 16.
Cf. A000244, A004656, A004658, A004659, ..., A004668: powers of 3 in base 10, 2, 4, 5, ..., 26.

Programs

  • Mathematica
    FromDigits[IntegerDigits[#,13]]&/@(3^Range[0,6]) (* Harvey P. Dale, Mar 05 2018 *)
  • PARI
    apply( a(n, b=13, m=3)=fromdigits(digits(m^n, b)), [0..6]) \\ This implements one possible continuation of the sequence beyond n = 6: write digits in decimal and carry over (so CC4 -> 12*100 + 12*10 + 4 = 1324). - M. F. Hasler, Jun 22 2018

A004669 Powers of 3 written in base 27.

Original entry on oeis.org

1, 3, 9, 10, 30, 90, 100, 300, 900, 1000, 3000, 9000, 10000, 30000, 90000, 100000, 300000, 900000, 1000000, 3000000, 9000000, 10000000, 30000000, 90000000, 100000000, 300000000, 900000000, 1000000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Similar to powers of 2 in base 8 (A004647) or 16 (A004655). - M. F. Hasler, Jun 22 2018

Links

Crossrefs

Cf. A000079, A004643, ..., A004655: powers of 2 written in base 10, 4, 5, ..., 16.
Cf. A000244, A004656, A004658, A004659, ..., A004668: powers of 3 in base 10, 2, 4, 5, ..., 26.

Programs

  • Mathematica
    Table[FromDigits[IntegerDigits[3^n, 27]], {n, 0, 100}] (* G. C. Greubel, Oct 12 2018 *)
  • PARI
    apply( a(n)=3^(n%3)*10^(n\3), [0..20]) \\ M. F. Hasler, Jun 22 2018

Formula

a(n) = 3^(n mod 3)*10^floor(n/3). - M. F. Hasler, Jun 22 2018
From Chai Wah Wu, Sep 03 2020: (Start)
a(n) = 10*a(n-3) for n > 2.
G.f.: (-9*x^2 - 3*x - 1)/(10*x^3 - 1). (End)

A129734 List of primitive prime divisors of the numbers 3^n-2^n (A001047) in their order of occurrence.

Original entry on oeis.org

5, 19, 13, 211, 7, 29, 71, 97, 1009, 11, 23, 331, 61, 53, 29927, 463, 3571, 17, 401, 129009091, 577, 1559, 745181, 4621, 43, 6217, 35839, 47, 2002867877, 5521, 101, 39756701, 79, 4057, 397760329, 369181, 68629840493971, 31, 241, 617671248800299, 3041, 14177
Offset: 1

Views

Author

N. J. A. Sloane, May 13 2007

Keywords

Comments

Read A001047 term-by-term, factorize each term, write down any primes not seen before.

Links

Crossrefs

Cf. A001047, A058765, A057468; A003462, A076481, A028491, A129733; A000225, A004668, A000043, A108974.

Extensions

a(41) and a(42) switched by Amiram Eldar, Jun 30 2023

A239661 Divisors of 1089.

Original entry on oeis.org

1, 3, 9, 11, 33, 99, 121, 363, 1089
Offset: 1

Views

Author

Omar E. Pol, Jun 10 2014

Keywords

Comments

Divisors of 33^2.
The sum of divisors of 1089 is equal to 1729, the Hardy-Ramanujan number: A000203(1089) = A001235(1) = 1729.
The aliquot divisors of 1089 are also the powers of 3 written in base 26, see A004668.
Also 1089 is widely used in magic tricks because it can be produced from any two three-digit numbers (see Links section).

Examples

			Sigma(1089) = 1 + 3 + 9 + 11 + 33 + 99 + 121 + 363 + 1089 = 1729.

Links

Crossrefs

Cf. A000203, A001235, A004668.

Programs

Showing 1-5 of 5 results.

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

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