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 1-10 of 13 results. Next

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).

A364780 Number of numbers with sum of digits n in fractional base 4/3.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 4, 3, 5, 6, 7, 14, 13, 15, 19, 19, 30, 39, 45, 56, 65, 75, 95, 124, 140, 174, 216, 268, 338, 417, 501, 627, 780, 974, 1203, 1454, 1825, 2266, 2769, 3427, 4268, 5188, 6433, 7930, 9671, 12000, 14738, 18265, 22642, 27961, 34528, 42523, 52325, 64425
Offset: 0

Views

Author

Kevin Ryde, Aug 13 2023

Keywords

Comments

Only a finite number of numbers have sum of digits n (the largest is A364779(n)).

Links

Crossrefs

Cf. A024631 (base 4/3), A244041 (sum of digits).
Cf. A357425 (smallest), A364779 (largest).
Cf. A245356 (count by length).

Programs

  • C
    /* See links */

A245400 Number of nonnegative integers with property that their base 9/8 expansion (see A024656) has n digits.

Original entry on oeis.org

9, 9, 9, 9, 9, 9, 9, 9, 9, 18, 18, 18, 18, 27, 27, 27, 36, 36, 45, 45, 54, 63, 72, 81, 90, 99, 108, 126, 144, 162, 180, 198, 225, 252, 288, 324, 360, 405, 459, 513, 576, 648, 729, 819, 927, 1044, 1170, 1314, 1485, 1665, 1872, 2106, 2376, 2673, 3006, 3384, 3807
Offset: 1

Views

Author

Tom Edgar, Jul 21 2014

Keywords

Examples

			a(2) = 9 since 80, 81, 82, 83, 84, 85, 86, 87, 88 are the base 9/8 representations of 9-17 respectively and these are the only integers with 2 digits.

Crossrefs

Cf. A245356, A120194, A024656, A081848.

Programs

  • Sage
    A=[1]
for i in [1..100]:
    A.append(ceil(((9-8)/8)*sum(A)))
[9*x for x in A]

Formula

a(n) = 9*A120194(n).

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).

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]

A245417 Number of nonnegative integers with property that their base 7/3 expansion (see A024640) has n digits.

Original entry on oeis.org

7, 14, 28, 70, 161, 378, 882, 2058, 4802, 11200, 26138, 60984, 142296, 332024, 774725, 1807694, 4217948, 9841881, 22964389, 53583572, 125028337, 291732784, 680709834, 1588322946, 3706086874, 8647536037, 20177584084, 47081029534, 109855735577, 256330049682
Offset: 1

Views

Author

Tom Edgar, Jul 21 2014

Keywords

Examples

			The only integers requiring two digits in base 7/3 are 30, 31, 32, 33, 34, 35, 36, 60, 61, 62, 63, 64, 65, 66, representing 7-20 respectively; thus, a(2) = 14.

Crossrefs

Cf. A245356, A081848, A024640.

Programs

  • Sage
    A=[1]
for i in [1..100]:
    A.append(ceil(((7-3)/3)*sum(A)))
[7*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]

A245420 Number of nonnegative integers with property that their base 8/5 expansion (see A024647) has n digits.

Original entry on oeis.org

8, 8, 16, 24, 40, 64, 96, 160, 256, 408, 648, 1040, 1664, 2664, 4264, 6816, 10912, 17456, 27928, 44688, 71496, 114400, 183040, 292864, 468576, 749728, 1199560, 1919296, 3070872, 4913400, 7861440, 12578304, 20125288, 32200456, 51520728, 82433168, 131893072
Offset: 1

Views

Author

Tom Edgar, Jul 21 2014

Keywords

Examples

			a(2) = 8 because 50, 51, 52, 53, 54, 55, 56, and 57 are the base 8/5 expansions for the numbers 8-15 respectively and these are the only integers with 2 digits.

Crossrefs

Cf. A024647, A245356, A081848.

Programs

  • Sage
    A=[1]
for i in [1..100]:
    A.append(ceil(((8-5)/5)*sum(A)))
[8*x for x in A]

A245425 Number of nonnegative integers with the property that their base 9/4 expansion (see A024652) has n digits.

Original entry on oeis.org

9, 18, 36, 81, 180, 405, 918, 2061, 4635, 10431, 23472, 52812, 118827, 267363, 601560, 1353510, 3045402, 6852150, 15417342, 34689015, 78050286, 175613148, 395129583, 889041555, 2000343501, 4500772875, 10126738971, 22785162687, 51266616048, 115349886108
Offset: 1

Views

Author

Tom Edgar, Jul 21 2014

Keywords

Examples

			The numbers 9-26 are represented by 40, 41, 42, 43, 44, 45, 46, 47, 48, 80, 81, 82, 83, 84, 85, 86, 87, 88 respectively in base 9/4. Since these are the only two digit integers we have a(2) = 18.

Crossrefs

Cf. A024652, A245356, A081848.

Programs

  • Sage
    A=[1]
for i in [1..100]:
    A.append(ceil(((9-4)/4)*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]
Showing 1-10 of 13 results. Next

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

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