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.

Previous Showing 21-26 of 26 results.

A245345 Sum of digits of n written in fractional base 9/2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 10, 4, 5, 6, 7, 8, 9, 10, 11, 12, 6, 7, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 15, 16, 3, 4, 5, 6, 7, 8, 9, 10, 11, 5, 6, 7, 8, 9, 10, 11, 12, 13, 7, 8, 9, 10, 11, 12, 13, 14, 15, 9, 10, 11, 12
Offset: 0

Views

Author

Tom Edgar, Jul 18 2014

Keywords

Comments

The base 9/2 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 9/2 the number 19 is represented by 41 and so a(19) = 4 + 1 = 5.

Links

Crossrefs

Cf. A000120, A007953, A024650, A053830, A244040.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[2 * Floor[n/9]] + Mod[n, 9]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\9 * 2) + n % 9); \\ Amiram Eldar, Aug 02 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(9,2,i) for i in [0..100]]

Formula

a(n) = A007953(A024650(n)).

A245350 Sum of digits of n written in fractional base 9/4.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 10, 11, 12, 8, 9, 10, 11, 12, 13, 14, 15, 16, 7, 8, 9, 10, 11, 12, 13, 14, 15, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17, 18, 14, 15, 16, 17, 18, 19, 20, 21, 22, 8, 9, 10, 11, 12, 13, 14, 15
Offset: 0

Views

Author

Tom Edgar, Jul 18 2014

Keywords

Comments

The base 9/4 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 9/4 the number 16 is represented by 47 and so a(16) = 4 + 7 = 11.

Links

Crossrefs

Cf. A000120, A007953, A024652, A053830, A244040.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/9]] + Mod[n, 9]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\9 * 4) + n % 9); \\ Amiram Eldar, Aug 02 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(9,4,i) for i in [0..100]]

Formula

a(n) = A007953(A024652(n)).

A245353 Sum of digits of n written in fractional base 9/7.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 8, 9, 10, 11, 12, 13, 14, 15, 12, 13, 14, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 21, 22, 23, 16, 17, 18, 19, 20, 21, 22, 23, 24, 23, 24, 25, 26, 27, 28, 29, 30, 31, 22, 23, 24, 25, 26, 27, 28, 29, 30, 27, 28, 29, 30, 31
Offset: 0

Views

Author

Hailey R. Olafson, Jul 18 2014

Keywords

Comments

The base 9/7 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 9/7 the number 14 is represented by 75 and so a(14) = 7 + 5 = 12.

Links

Crossrefs

Cf. A000120, A007953, A024655, A053830, A244040.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[7 * Floor[n/9]] + Mod[n, 9]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\9 * 7) + n % 9); \\ Amiram Eldar, Aug 02 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(9,7,w) for w in [0..200]]

Formula

a(n) = A007953(A024655(n)).

A245354 Sum of digits of n in fractional base 9/5.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 16, 17, 18, 19, 8, 9, 10, 11, 12, 13, 14, 15, 16, 13, 14, 15, 16, 17, 18, 19, 20, 21, 14, 15, 16, 17, 18, 19, 20, 21, 22, 19, 20, 21, 22, 23
Offset: 0

Views

Author

James Van Alstine, Jul 18 2014

Keywords

Comments

The base 9/5 expansion is unique, and thus the sum of digits function is well-defined.

Examples

			In base 9/5 the number 11 is represented by 52 and so a(11) = 5 + 2 = 7.

Links

Crossrefs

Cf. A007953, A024653, A053830.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/9]] + Mod[n, 9]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\9 * 4) + n % 9); \\ Amiram Eldar, Aug 02 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(9,5,y) for y in [0..200]]

Formula

a(n) = A007953(A024653(n)). - Amiram Eldar, Aug 02 2025

A239695 Base 9 sum of digits of prime(n).

Original entry on oeis.org

2, 3, 5, 7, 3, 5, 9, 3, 7, 5, 7, 5, 9, 11, 7, 13, 11, 13, 11, 15, 9, 15, 3, 9, 9, 5, 7, 11, 5, 9, 7, 11, 9, 11, 13, 15, 13, 3, 7, 5, 11, 5, 7, 9, 13, 7, 11, 15, 11, 13, 17, 15, 17, 11, 9, 7, 13, 7, 13, 9, 11, 13, 11, 15, 17, 13, 11, 9, 11, 13, 9, 15, 15, 13, 11
Offset: 1

Views

Author

Tom Edgar, Mar 24 2014

Keywords

Comments

a(n) is the rank of prime(n) in the base-9 dominance order on the natural numbers.

Examples

			The fifth prime is 11, 11 in base 9 is (1,2) so a(5)=1+2=3.

Links

Crossrefs

Cf. A007605, A014499, A053830, A239690, A239691, A239692, A239693, A239694.

Programs

  • Magma
    [&+Intseq(NthPrime(n),9): n in [1..100]]; // Vincenzo Librandi, Mar 25 2014
  • Mathematica
    Table[Plus @@ IntegerDigits[Prime[n], 9], {n, 1, 100}] (* Vincenzo Librandi, Mar 25 2014 *)
  • PARI
    a(n) = sumdigits(prime(n), 9); \\ Michel Marcus, Mar 04 2023
  • Sage
    [sum(i.digits(base=9)) for i in primes_first_n(200)]

Formula

a(n) = A053830(A000040(n)).

A037334 Numbers whose base-8 and base-9 expansions have the same digit sum.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 120, 121, 122, 123, 124, 125, 176, 177, 178, 179, 234, 235, 236, 237, 238, 239, 288, 289, 290, 291, 292, 293, 294, 295, 344, 345, 346, 347, 348, 349, 350, 459, 460, 461, 462, 463, 568, 569, 570, 571, 572, 573
Offset: 1

Views

Author

Clark Kimberling

Keywords

Examples

			125 is in the sequence because 125 = (1,4,8)_9 = (1,7,5)_8 and 1+4+8 = 1+7+5. 126 is not in the sequence because 126 = (1,5,0)_9 = (1,7,6)_8 but 1+5+0 <> 1+7+6. - _R. J. Mathar_, Jun 30 2021

Crossrefs

Cf. A053829, A053830.

Formula

{n: A053829(n) = A053830(n)}. - R. J. Mathar, Jun 30 2021
Previous Showing 21-26 of 26 results.

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