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.

User: James Van Alstine

James Van Alstine's wiki page.

James Van Alstine has authored 17 sequences. Here are the ten most recent ones:

A245423 Number of nonnegative integers with property that their base 7/5 expansion (see A024642) has n digits.

Original entry on oeis.org

7, 7, 7, 14, 14, 21, 28, 42, 56, 84, 112, 161, 224, 315, 441, 616, 861, 1204, 1687, 2366, 3311, 4634, 6489, 9086, 12719, 17808, 24927, 34902, 48860, 68404, 95767, 134071, 187698, 262780, 367892, 515046, 721070, 1009498, 1413293, 1978613, 2770054, 3878077
Offset: 1

Views

Author

James Van Alstine, Jul 21 2014

Keywords

Examples

			The numbers 7-13 are represented by 50, 51, 52, 53, 54, 55, 56 respectively in base 7/5. These are the only integers with two digits, and so a(2)=7.

Crossrefs

Cf. A024642, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((7-5)/5*sum(A)))
[7*x for x in A]

A245419 Number of nonnegative integers with property that their base 8/3 expansion (see A024645) has n digits.

Original entry on oeis.org

8, 16, 40, 112, 296, 792, 2112, 5632, 15016, 40040, 106776, 284736, 759296, 2024792, 5399440, 14398512, 38396032, 102389416, 273038440, 728102512, 1941606696, 5177617856, 13806980952, 36818615872, 98182975656, 261821268416, 698190049112, 1861840130960
Offset: 1

Views

Author

James Van Alstine, Jul 21 2014

Keywords

Examples

			The numbers 8-23 are represented by 30, 31, 32, 33, 34, 35, 36, 37, 60, 61, 62, 63, 64, 65, 66, 67 respectively in base 8/3. These are the only integers with two digits, and so a(2)=16.

Crossrefs

Cf. A024645, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((8-3)/3*sum(A)))
[8*x for x in A]

A245416 Number of nonnegative integers with property that their base 9/2 expansion (see A024650) has n digits.

Original entry on oeis.org

9, 36, 162, 729, 3276, 14742, 66339, 298530, 1343385, 6045228, 27203526, 122415867, 550871406, 2478921327, 11155145967, 50198156856, 225891705852, 1016512676334, 4574307043503, 20584381695759, 92629717630920, 416833729339140, 1875751782026130
Offset: 1

Views

Author

James Van Alstine, Jul 21 2014

Keywords

Examples

			The numbers 9-44 are represented by 20, 21, 22, 23, 24, 25, 26, 27, 28, 40, 41, 42, 43, 44, 45, 46, 47, 48, 60, 61, 62, 63, 64, 65, 66, 67, 68, 80, 81, 82, 83, 84, 85, 86, 87, 88 respectively in base 9/2. These are the only integers with two digits, and so a(2)=36.

Crossrefs

Cf. A024650, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((9-2)/2*sum(A)))
[9*x for x in A]

A245404 Number of nonnegative integers with property that their base 7/2 expansion (see A024639) has n digits.

Original entry on oeis.org

7, 21, 70, 245, 861, 3010, 10535, 36876, 129066, 451731, 1581055, 5533696, 19367936, 67787776, 237257216, 830400256, 2906400896, 10172403136, 35603410976, 124611938416, 436141784456, 1526496245596, 5342736859586, 18699579008551, 65448526529925, 229069842854741
Offset: 0

Views

Author

James Van Alstine, Jul 21 2014

Keywords

Examples

			The numbers 7-27 are represented by 20, 21, 22, 23, 24, 25, 26, 40, 41, 42, 43, 44, 45, 46, 60, 61, 62, 63, 64, 65, 66 respectively in base 7/2. These are the only integers with two digits, and so a(2)=21.

Crossrefs

Cf. A024639, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((7-2)/2*sum(A)))
[7*x for x in A]

A245403 Number of nonnegative integers with property that their base 10/9 expansion (see A024664) has n digits.

Original entry on oeis.org

10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 30, 30, 30, 40, 40, 50, 50, 60, 60, 70, 80, 90, 100, 110, 120, 130, 150, 160, 180, 200, 220, 250, 280, 310, 340, 380, 420, 470, 520, 580, 640, 710, 790, 880, 980, 1090, 1210, 1340, 1490, 1660
Offset: 1

Views

Author

James Van Alstine, Jul 21 2014

Keywords

Examples

			The numbers 10-19 are represented by 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 respectively in base 10/9. These are the only integers with two digits, and so a(2)=10.

Crossrefs

Cf. A024664, A120202, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((10-9)/9*sum(A)))
[10*x for x in A]

Formula

a(n) = 10*A120202(n).

A245401 Number of nonnegative integers with property that their base 8/7 expansion (see A024649) has n digits.

Original entry on oeis.org

8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 24, 24, 32, 32, 40, 40, 48, 56, 64, 72, 80, 96, 112, 128, 144, 160, 184, 216, 240, 280, 320, 360, 416, 472, 544, 616, 704, 808, 920, 1056, 1208, 1376, 1576, 1800, 2056, 2352, 2688, 3072, 3512, 4008, 4584
Offset: 1

Views

Author

James Van Alstine, Jul 21 2014

Keywords

Comments

The numbers 8-15 are represented by 70, 71, 72, 73, 74, 75, 76, 77 respectively in base 8/7. These are the only integers with two digits, and so a(2)=8.

Crossrefs

Cf. A081848, A024649, A120186.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((8-7)/7*sum(A)))
[8*x for x in A]

Formula

a(n) = 8*A120186(n).

A245426 Number of nonnegative integers with property that their base 7/4 expansion (see A024641) has n digits.

Original entry on oeis.org

7, 7, 14, 21, 42, 70, 126, 217, 378, 665, 1162, 2037, 3563, 6237, 10913, 19096, 33418, 58485, 102347, 179109, 313439, 548520, 959910, 1679839, 2939720, 5144510, 9002889, 15755061, 27571355, 48249873, 84437276, 147765233, 258589156, 452531023, 791929292
Offset: 1

Views

Author

James Van Alstine, Jul 21 2014

Keywords

Examples

			The numbers 7-13 are represented by 40, 41, 42, 43, 44, 45, 46 respectively in base 7/4. These are the only integers with two digits, and so a(2)=7.

Crossrefs

Cf. A024641, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((7-4)/4*sum(A)))
[7*x for x in A]

A245357 Number of numbers whose base 5/4 expansion (see A024634) has n digits.

Original entry on oeis.org

5, 5, 5, 5, 5, 10, 10, 15, 15, 20, 25, 30, 40, 50, 60, 75, 95, 120, 150, 185, 235, 290, 365, 455, 570, 710, 890, 1110, 1390, 1735, 2170, 2715, 3390, 4240, 5300, 6625, 8280, 10350, 12940, 16175, 20215, 25270, 31590, 39485, 49355, 61695, 77120, 96400, 120500
Offset: 1

Views

Author

James Van Alstine, Jul 18 2014

Keywords

Examples

			The numbers 10..14 are represented by 430, 431, 432, 433, 434 respectively in base 5/4. These are the only numbers with three digits, and so a(3)=5.

Links

Crossrefs

Cf. A024634, A120160, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil((5-4)/4*sum(A)))
[5*x for x in A]

Formula

a(n) = 5*A120160(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

A245349 Sum of digits of n written in fractional base 7/4.

Original entry on oeis.org

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

Views

Author

James Van Alstine, Jul 18 2014

Keywords

Comments

The base 7/4 expansion is unique, and thus the sum of digits function is well-defined.

Examples

			In base 7/4 the number 7 is represented by 40 and so a(7) = 4 + 0 = 4.

Links

Crossrefs

Cf. A024641, A053828, A007953.

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 0, 0, a[4 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)
  • PARI
    a(n) = if(n == 0, 0, a(n\7 * 4) + n % 7); \\ Amiram Eldar, Jul 31 2025
  • Sage
    # uses [basepqsum from A245355]
[basepqsum(7,4,y) for y in [0..200]]

Formula

a(n) = A007953(A024641(n)). - Amiram Eldar, Jul 31 2025

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

Content is available under The OEIS End-User License Agreement.