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 1-5 of 5 results.

A077340 Final terms of rows in A077339.

Original entry on oeis.org

1, 20, 31, 42, 53, 64, 75, 86, 97, 108, 119, 1200, 1301, 1402, 1503, 1604, 1705, 1806, 1907, 2008, 2109, 2210, 2311, 2412, 2513, 2614, 2715, 2816, 2917, 3018, 3119, 3220, 3321, 3422, 3523, 3624, 3725, 3826, 3927, 4028
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2002

Keywords

Comments

n-th number beginning with n. Can anyone derive a formula for a(n)?

Links

Crossrefs

Cf. A077339, A077341, A077342, A077343.

Programs

Formula

From Robert Israel, Aug 08 2018: (Start)
a(m+(10^k+8)/9) = 10^k*(m+(10^k+8)/9)+m for 0 <= m < 10^k.
G.f.: (1-x)^(-2)*(x+x^2 + Sum_{k>=1} ((10^(2*k-1)+7*10^(k-1))*x^((10^k+8)/9) + (-10^(2*k-1)+2*10^(k-1))*x^((10^k+17)/9))).
(End)

Extensions

Definition corrected by M. F. Hasler, Jan 07 2013

A081929 Sum of the n-th row of A077339.

Original entry on oeis.org

1, 22, 64, 127, 211, 316, 442, 589, 757, 946, 1156, 2467, 3979, 5692, 7606, 9721, 12037, 14554, 17272, 20191, 23311, 26632, 30154, 33877, 37801, 41926, 46252, 50779, 55507, 60436, 65566, 70897, 76429, 82162, 88096, 94231, 100567, 107104
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2003

Keywords

Links

Crossrefs

Not the same as A069178 (A069178(12)=1387 <> 2467=a(12) ). Cf. A077339, A077340.

Formula

For n>10, a(n) = 1/2 * (201n^2 - 2001n + 2).
From Chai Wah Wu, Jan 12 2023: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 13.
G.f.: x*(900*x^12 - 1080*x^11 - x^2 - 19*x - 1)/(x - 1)^3. (End)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

A077341 Triangle in which n-th row contains the first n numbers, not already present, that begin with n.

Original entry on oeis.org

1, 2, 20, 3, 30, 31, 4, 40, 41, 42, 5, 50, 51, 52, 53, 6, 60, 61, 62, 63, 64, 7, 70, 71, 72, 73, 74, 75, 8, 80, 81, 82, 83, 84, 85, 86, 9, 90, 91, 92, 93, 94, 95, 96, 97, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2002

Keywords

Comments

Every positive number appears exactly once. Proof: N will appear as the first term of row N, unless it has already appeared. And no term is repeated, by definition.
The first term of the 20th row is 200 unlike the 20th row of A077339 where it is 20.

Examples

			Triangle begins:
1
2 20
3 30 31
4 40 41 42
5 50 51 52 53
...

Links

Crossrefs

Cf. A077339, A077340 (see there for differences), A077342, A077343.

Programs

  • PARI
    {u=[];for(m=1,19,o=0;for(n=1,m,while(setsearch(u,a=A077339(m,n+o)),o++);u=setunion(u,Set(a));print1(a",")))} \\ M. F. Hasler, Jan 08 2013

Extensions

Edited by N. J. A. Sloane, Jun 12 2007

A077343 Final terms of rows in A077341.

Original entry on oeis.org

1, 20, 31, 42, 53, 64, 75, 86, 97, 108, 119, 1200, 1301, 1402, 1503, 1604, 1705, 1806, 1907, 2009, 2109, 2210, 2311, 2412, 2513, 2614, 2715, 2816, 2917, 3019, 3120, 3220, 3321, 3422, 3523, 3624, 3725, 3826, 3927, 4029, 4130, 4231, 4331, 4432, 4533, 4634, 4735, 4836, 4937, 5039
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2002

Keywords

Comments

Differs from A077340 in a(20), a(30), a(31), a(40..42), a(50..53), ... - M. F. Hasler, Jan 07 2013

Links

Crossrefs

Cf. A077339, A077340, A077341, A077342.

Programs

  • PARI
    {u=[];for(m=1,199,o=0;for(n=1,m,while(setsearch(u,a=A077339(m,n+o)),o++);u=setunion(u,Set(a)));print1(a","))} \\ - M. F. Hasler, Jan 07 2013

Extensions

More terms from M. F. Hasler, Jan 07 2013

A077342 First column of A077341.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 200, 21, 22, 23, 24, 25, 26, 27, 28, 29, 300, 310, 32, 33, 34, 35, 36, 37, 38, 39, 400, 410, 420, 43, 44, 45, 46, 47, 48, 49, 500, 510, 520, 530, 54, 55, 56, 57, 58, 59, 600, 610, 620, 630, 640, 65, 66, 67
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2002

Keywords

Comments

a(20) = 200 and not 20. Can anyone derive a formula for a(n)?
a(n) = n when n > 10 * floor(n/10) + floor(n/10) - 2. Otherwise it is guaranteed that n has appeared in a previous row of the triangle. - Alonso del Arte, Jan 07 2013

Links

Crossrefs

Cf. A077339, A077340, A077341, A077343.
Showing 1-5 of 5 results.

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

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