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: Dan Hoey

Dan Hoey's wiki page.

Dan Hoey has authored 77 sequences. Here are the ten most recent ones:

A143789 Lightest finite monotonically increasing sequence obtained by chunking an 18-digit Skolem-Langford integer (see A108116). There are d digits between two d's in the sequence.

Original entry on oeis.org

4, 5, 6, 7, 8, 41, 51, 63, 72, 83, 200
Offset: 1

Views

Author

Dan Hoey and Eric Angelini, Sep 01 2008

Keywords

Comments

"Lightest" --> the weight of such a sequence is the sum of all its terms; "Finite" --> by definition all such sequences are finite; "Monotonically" --> no two adjacent terms in the sequence are the same; "Increasing" --> a(n) < a(n+1); "Chunking" --> cutting in slices. The original Skolem-Langford number is 456784151637283200 [this is a(14565) in "D. Wilson, Complete table of n, a(n) for n = 1..20120", which can be found at A108116] and this integer, properly chunked, produces the sequence]. In the sequence there is no digit between the two 0's, there is one digit between the two 1's, there are two digits between the two 2's,... there are eight digits between the two 8's. This sequence has been computed by Dan Hoey.

Crossrefs

Cf. A108116 and A132291

A094101 Number of rooted 8-dimensional "polycubes" with n cells, with no symmetries removed.

Original entry on oeis.org

1, 16, 360, 9104, 246020, 6940128, 201819688, 6003642144, 181770021702, 5581576203840, 173384554507648, 5438172832075920
Offset: 1

Views

Author

Dan Hoey

Keywords

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Links

Crossrefs

Row 8 of A048790.
Cf. A094100, A048663-A048868, A151834.

Formula

a(n) = n * A151834(n). - Andrew Howroyd, Dec 05 2018

Extensions

a(9)-a(12) from Andrew Howroyd, Dec 05 2018

A094100 Fit a polynomial of degree k-1 to column k of array in A048790, evaluate it at dimension n = -1.

Original entry on oeis.org

1, -2, 9, -64, 560, -5370, 53788, -555864, 5957685, -66459200, 763983132, -8919566196, 105678848821, -1286858544734
Offset: 1

Views

Author

Dan Hoey

Keywords

Comments

Might be thought of as number of rooted (-1)-dimensional "polycubes" with n cells, with no symmetries removed.

References

  • Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Links

Crossrefs

Cf. A094101, A048663-A048868.

Extensions

a(9)-a(14) using Luther & Mertens's formulas added by Andrei Zabolotskii, Jun 27 2025

A051813 Number of n-digit numbers with nonzero multiplicative digital root 2.

Original entry on oeis.org

1, 15, 208, 2389, 24845, 243697, 2348885, 22837227, 226507501, 2285904554, 23239957877, 235731610792, 2372897841904, 23686630752065, 235058927877399, 2327977363798607
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051804, A051822.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=2 }

A051814 Number of n-digit numbers with nonzero multiplicative digital root 3.

Original entry on oeis.org

1, 7, 40, 240, 1448, 8630, 53545, 371845, 3267453, 36428242, 442762543, 5217693527, 57321559329, 586532407659, 5666269188709, 52728701479194
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051805, A051823.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=3 }

A051815 Number of n-digit numbers with nonzero multiplicative digital root 4.

Original entry on oeis.org

1, 12, 105, 780, 5452, 39979, 336081, 3263355, 34518027, 372779338, 3957184040, 40729856248, 406862880846, 3979167973684, 38556471560342, 374259579575061
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051806, A051824.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=4 }

A051816 Number of n-digit numbers with nonzero multiplicative digital root 5.

Original entry on oeis.org

1, 7, 58, 422, 2872, 19772, 142418, 1096582, 9040811, 78452199, 699839588, 6297456806, 56804155533, 517737762700, 4839960759976, 46837953974511
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051807, A051825.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=5 }

A051817 Number of n-digit numbers with nonzero multiplicative digital root 6.

Original entry on oeis.org

1, 14, 198, 2124, 20894, 208420, 2117454, 21576952, 218613631, 2195038525, 21848423462, 216219614463, 2135812278843, 21121667130245, 209377570378397, 2080106337706143
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051808, A051826.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=6 }

A051818 Number of n-digit numbers with nonzero multiplicative digital root 7.

Original entry on oeis.org

1, 3, 14, 86, 666, 6418, 64079, 597445, 5116146, 40671872, 304752986, 2187716324, 15395364971, 110611591118, 866239098731, 7907500662596
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051809, A051827.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=7 }

A051819 Number of n-digit numbers with nonzero multiplicative digital root 8.

Original entry on oeis.org

1, 23, 228, 2536, 29135, 320182, 3348887, 33918043, 337681353, 3346457531, 33328331754, 335156871449, 3402031164396, 34729171765901, 354926411492071, 3618033042193311
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051810, A051828.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=8 }

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