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 1-4 of 4 results.

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.

A077339 Triangle in which n-th row contains the first n numbers beginning 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
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2002

Keywords

Comments

Repetitions are allowed.
The first term in row m is T(m,1)=m, followed by T(m,2)=10m, 10m+1,..., 10m+9; then, T(m,12)=100m, 100m+1, ..., 100m+99, then T(m,112)=1000m,...,1000m+999, etc. (as long as the second index does not exceed the first, given the definition of this triangular sequence. But in principle one can consider the n-th number "starting with m" without that restriction). The first repetitions to occur seem to be T(20,1)=20=T(2,2), T(30,1)=30=T(3,2), T(31,1)=31=T(3,3), ... These cause the differences with A077341, and also the differences between A077340 and A077343. - M. F. Hasler, Jan 07 2013

Examples

			The triangle starts:
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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 1200; ...

Crossrefs

Cf. A077340. Different from A077341.

Programs

  • PARI
    A077339(m,n,p=1)={!n & n=m+(1-m=(sqrtint(8*m-7)+1)\2)*m\2; while(n>p,n-=p;p*=10);p*m+n-1} \\ returns the n-th number starting with m, allowing also n>m (useful for A077341 ff), or the m-th term of the sequence, if no 2nd arg is given. \\ - M. F. Hasler, Jan 07 2013

Extensions

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

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
Showing 1-4 of 4 results.

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

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