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: Hailey R. Olafson

Hailey R. Olafson's wiki page.

Hailey R. Olafson has authored 17 sequences. Here are the ten most recent ones:

A245477 Period 6: repeat [1, 1, 1, 1, 1, 2].

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1
Offset: 0

Views

Author

Hailey R. Olafson, Jul 23 2014

Keywords

Comments

First differences of A047368. The first differences of this sequence are in A131533. - Wesley Ivan Hurt, Jul 24 2014
Binomial Transform of a(n) gives: 1, 2, 4, 8, 16, 33, 70, 149, 312, 638, 1276, 2511, ... - Wesley Ivan Hurt, Aug 13 2014

Links

Crossrefs

Cf. A024643, A047368, A097325, A130782, A131534, A172051, A177702, A177704, A177706.

Programs

  • Magma
    [Floor((n+1)*7/6) - Floor((n)*7/6) : n in [0..100]]; // Wesley Ivan Hurt, Aug 06 2014
  • Maple
    A:= n -> piecewise(n mod 6 = 5, 2, 1);
seq(A(n), n=0..100); # Robert Israel, Jul 23 2014
  • Mathematica
    Table[2 - Sign[Mod[n + 1, 6]], {n, 0, 100}] (* Wesley Ivan Hurt, Jul 24 2014 *)
PadRight[{},120,{1,1,1,1,1,2}] (* Harvey P. Dale, Jun 02 2016 *)
  • PARI
    a(n) = 7*(n+1)\6 - 7*n\6; \\ Michel Marcus, Jul 23 2014
  • Sage
    [floor((n+1)*7/6) - floor((n)*7/6) for n in [0..200]]

Formula

a(n) = floor((n+1)*7/6) - floor((n)*7/6).
G.f.: 1/(1-x) + x^5/(1-x^6). - Robert Israel, Jul 23 2014
From Wesley Ivan Hurt, Jul 24 2014, Aug 06-29 2014: (Start)
a(n) = 2 - sign((n+1) mod 6).
a(n) = 3 - 2^sign((n+1) mod 6).
a(n) = A172051(n) + 1.
a(2n) = 1, a(2n+1) = A177702(n).
Sum_{i=0..n-2} a(i) = A047368(n), n>0.
a(n) = 1 + mod(n, 1 + mod(n-1, 3)).
a(n) = 1 + binomial(mod(5n + 10, 6), 5). (End)
From Wesley Ivan Hurt, Jun 23 2016: (Start)
a(n) = a(n-6) for n>5.
a(n) = (7 - cos(n*Pi) + cos(n*Pi/3) - cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/6. (End)

A245429 Number of nonnegative integers with property that their base 9/7 expansion (see A024655) has n digits.

Original entry on oeis.org

9, 9, 9, 9, 18, 18, 27, 36, 45, 54, 72, 90, 117, 153, 198, 252, 324, 414, 531, 684, 882, 1134, 1458, 1872, 2412, 3096, 3978, 5121, 6579, 8460, 10881, 13986, 17982, 23121, 29727, 38223, 49140, 63180, 81234, 104445, 134280, 172647, 221976, 285399, 366939, 471780
Offset: 1

Views

Author

Hailey R. Olafson, Jul 21 2014

Keywords

Examples

			a(2) = 9 because 70, 71, 72, 73, 74, 75, 76, 77 and 78 are the base 9/7 expansions for the integers 9, 10, 11, 12, 13, 14, 15, 16 and 17 respectively and these are the only integers with 2 digits.

Crossrefs

Cf. A024655, A081848, A245356.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((9-7)/7)*sum(A)))
[9*x for x in A]

A245428 Number of nonnegative integers with property that their base 10/3 expansion (see A024658) has n digits.

Original entry on oeis.org

10, 30, 100, 330, 1100, 3670, 12230, 40770, 135900, 453000, 1510000, 5033330, 16777770, 55925900, 186419660, 621398870, 2071329570, 6904431900, 23014773000, 76715910000, 255719700000, 852399000000, 2841330000000, 9471100000000, 31570333333330, 105234444444430
Offset: 1

Views

Author

Hailey R. Olafson, Jul 21 2014

Keywords

Examples

			a(2) = 30 because 30, 31,.., 60, 61, .., 98 and 99 are the base 10/3 expansions for the integers 10, 11, .., 20, 21,.., 38, and 39 respectively and these are the only integers with 2 digits.

Crossrefs

Cf. A024658, A081848, A245356.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((10-3)/3)*sum(A)))
[10*x for x in A]

A245418 Number of nonnegative integers with property that their base 5/3 expansion (see A024633) has n digits.

Original entry on oeis.org

5, 5, 10, 15, 25, 40, 70, 115, 190, 320, 530, 885, 1475, 2460, 4100, 6830, 11385, 18975, 31625, 52710, 87850, 146415, 244025, 406710, 677850, 1129750, 1882915, 3138190, 5230320, 8717200, 14528665, 24214440, 40357400, 67262335, 112103890, 186839820, 311399700
Offset: 1

Views

Author

Hailey R. Olafson, Jul 21 2014

Keywords

Examples

			a(2) = 5 because 30, 31, 32, 33 and 34 are the base 5/3 expansions for the integers 5, 6, 7, 8 and 9 respectively and these are the only integers with 2 digits.

Crossrefs

Cf. A024633, A245356, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((5-3)/3)*sum(A)))
[5*x for x in A]

A245415 Number of nonnegative integers with property that their base 5/2 expansion (see A024632) has n digits.

Original entry on oeis.org

5, 10, 25, 60, 150, 375, 940, 2350, 5875, 14685, 36715, 91785, 229465, 573660, 1434150, 3585375, 8963440, 22408600, 56021500, 140053750, 350134375, 875335935, 2188339840, 5470849600, 13677124000, 34192810000, 85482025000, 213705062500, 534262656250
Offset: 1

Views

Author

Hailey R. Olafson, Jul 21 2014

Keywords

Examples

			a(2) = 10 because  20, 21, 22, 23, 24, 40, 41, 42, 43 and 44 are the base 5/2 expansions for the integers 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14 respectively and these are the only integers with 2 digits.

Crossrefs

Cf. A081848, A245356, A024632.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((5-2)/2)*sum(A)))
[5*x for x in A]

A245402 Number of nonnegative integers with property that their base 7/6 expansion (see A024643) has n digits.

Original entry on oeis.org

7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 21, 21, 28, 28, 35, 42, 49, 56, 63, 77, 91, 105, 119, 140, 161, 189, 224, 259, 301, 350, 413, 483, 560, 651, 763, 889, 1036, 1211, 1414, 1645, 1925, 2240, 2618, 3052, 3563, 4158, 4851, 5656, 6601, 7700, 8981, 10479, 12229, 14266
Offset: 1

Views

Author

Hailey R. Olafson, Jul 21 2014

Keywords

Examples

			a(3) = 7 because 650, 651, 652, 653, 654, 655 and 656 are the base 7/6 expansions for the integers 14, 15, 16, 17, 18, 19 and 20 respectively and these are the only integers with 3 digits.

Crossrefs

Cf. A024643, A120178, A072493, A245356.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((7-6)/6)*sum(A)))
[7*x for x in A]

Formula

a(n) = 7*A120178(n).

A245399 Number of nonnegative integers with property that their base 6/5 expansion (see A024638) has n digits.

Original entry on oeis.org

6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 18, 24, 30, 36, 42, 48, 60, 72, 84, 102, 126, 150, 180, 216, 258, 312, 372, 444, 534, 642, 768, 924, 1110, 1332, 1596, 1914, 2298, 2760, 3312, 3972, 4770, 5724, 6864, 8238, 9888, 11862, 14238, 17082, 20502, 24600, 29520, 35424
Offset: 1

Views

Author

Hailey R. Olafson, Jul 21 2014

Keywords

Examples

			a(3) = 6 because 540, 541, 542, 543, 544 and 545 are the base 6/5 expansions for the integers 12, 13, 14, 15, 16 and 17 respectively and these are the only integers with 3 digits.

Links

Crossrefs

Cf. A024638, A081848, A120170, A245356.

Programs

  • Mathematica
    A120170[n_]:= A120170[n] = If[n==1, 1, Ceiling[Sum[A120170[j], {j, n-1}]/5]]; Table[6*A120170[n], {n, 60}] (* G. C. Greubel, Aug 19 2019 *)
  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((6-5)/5)*sum(A)))
[6*x for x in A]

Formula

a(n) = 6*A120170(n).

A245431 Number of nonnegative integers with property that their base 10/7 expansion has n digits.

Original entry on oeis.org

10, 10, 10, 20, 30, 40, 60, 80, 120, 170, 240, 340, 490, 700, 1000, 1430, 2040, 2910, 4160, 5940, 8490, 12130, 17330, 24750, 35360, 50520, 72170, 103100, 147280, 210400, 300570, 429390, 613410, 876300, 1251860, 1788370, 2554820, 3649740, 5213910, 7448450
Offset: 1

Views

Author

Hailey R. Olafson, Jul 21 2014

Keywords

Comments

See A024662 for an explanation of base 10/7.

Examples

			a(2) = 10 because 70, 71, 72, 73, 74, 75, 76, 77, 78 and 79 are the base 10/7 expansions for the integers 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19 respectively and these are the only integers with 2 digits.

Crossrefs

Cf. A024662, A081848, A245356.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((10-7)/7)*sum(A)))
[10*x for x in A]

A245356 Number of numbers whose base-4/3 expansion (see A024631) has n digits.

Original entry on oeis.org

4, 4, 4, 4, 8, 8, 12, 16, 20, 28, 36, 48, 64, 88, 116, 156, 208, 276, 368, 492, 656, 872, 1164, 1552, 2068, 2760, 3680, 4904, 6540, 8720, 11628, 15504, 20672, 27560, 36748, 48996, 65328, 87104, 116140, 154852, 206472, 275296, 367060, 489412, 652552, 870068
Offset: 1

Views

Author

Hailey R. Olafson, Jul 18 2014

Keywords

Examples

			a(3) = 4 because 320, 321, 322, and 323 are the base-4/3 expansions for the numbers 9, 10, 11, and 12 respectively and these are the only numbers with 3 digits.

Crossrefs

Cf. A072493, A024631, A081848.

Programs

  • Sage
    A=[1]
for i in [1..60]:
    A.append(ceil(((4-3)/3)*sum(A)))
[4*x for x in A]

Formula

a(n) = 4*A072493(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)).

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