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.

A081968 Duplicate of A076096.

Original entry on oeis.org

1, 8, 18, 9261000, 329422500, 13456677968449745006250
Offset: 1

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Author

Keywords

A076097 Products of rows in A076099.

Original entry on oeis.org

1, 16, 216, 1944810000, 3913539300000, 9992390792252042651841000000, 1068203306732039166959846576540631630000000, 1316372224808054302435728765171857144838608100000000
Offset: 1

Views

Author

Amarnath Murthy, Oct 08 2002

Keywords

Crossrefs

Cf. A076027, A076028, A076029, A076030, A076031, A076095, A076096, A076098, A076099.

Extensions

More terms from David Wasserman, Apr 01 2005
Edited by Ray Chandler, May 09 2007
Offset corrected by Sean A. Irvine, Mar 19 2025

A076098 Geometric mean of n-th row in A076099.

Original entry on oeis.org

1, 4, 6, 210, 330, 46410, 1009470, 2454270, 358888530, 8804809860, 14908423530, 87770875982790, 8644083578130, 6461153376929140890, 55507010099631090, 435066914019898690530, 12624989405621802949740, 1768322825403098494530
Offset: 0

Views

Author

Amarnath Murthy, Oct 08 2002

Keywords

Crossrefs

Cf. A076027, A076028, A076029, A076030, A076031, A076095, A076096, A076097, A076099.

Formula

a(n)= A076097(n)^(1/n).

Extensions

More terms from David Wasserman, Apr 01 2005
Edited by Ray Chandler, May 09 2007
Offset corrected by Sean A. Irvine, Mar 19 2025

A076099 Triangle read by rows in which the n-th row contains n numbers not occurring in the previous rows whose product is an n-th power. The first (n-1) numbers of the n-th row are the smallest number not occurring earlier and the n-th term is chosen to satisfy the requirement.

Original entry on oeis.org

1, 2, 8, 3, 4, 18, 5, 6, 7, 9261000, 9, 10, 11, 12, 329422500, 13, 14, 15, 16, 17, 13456677968449745006250, 19, 20, 21, 22, 23, 24, 11022732501667945875061568782593750, 25, 26, 27, 28, 29, 30, 31
Offset: 1

Views

Author

Amarnath Murthy, Oct 08 2002

Keywords

Comments

Another rearrangement of the natural numbers in which the product of next n numbers is an n-th power.
The first n-1 elements of the n-th group are the smallest n-1 numbers that haven't already appeared, say u1, u2, ..., u_(n-1) and let u_n be the unknown final element of the n-th group. Let u1*u2*u3*...*u_(n-1) = (p1^e1)(p2^e2)...(pr^er). Then u_n = product(i=1 to r) p_i^(ei + n*floor(ei/n) - n) ...unless this has already appeared in the sequence (probably this never happens). More simply, I conjecture that u_n = product(i=1 to r) p_i^(ei - n). - Sam Alexander, Dec 31 2003

Examples

			Triangle begins:
1
2 8
3 4 18
5 6 7 9261000
9 10 11 12 329422500
...

Crossrefs

Cf. A076027, A076028, A076029, A076030, A076031, A076095, A076096, A076097, A076098.

Extensions

Corrected and extended by Sam Alexander, Dec 31 2003
Edited by Ray Chandler, May 09 2007
Offset corrected by Sean A. Irvine, Mar 19 2025

A076095 Initial terms of rows in A076099.

Original entry on oeis.org

1, 2, 3, 5, 9, 13, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907, 950, 994, 1039, 1085, 1132, 1180, 1229, 1279, 1330, 1382
Offset: 1

Views

Author

Amarnath Murthy, Oct 07 2002

Keywords

Comments

This sequence is not the same as A076027.

Crossrefs

Cf. A076027, A076028, A076029, A076030, A076031, A076096, A076097, A076098, A076099.

Extensions

More terms from David Wasserman, Apr 01 2005
Edited by Ray Chandler, May 09 2007
Offset corrected by Sean A. Irvine, Mar 19 2025
Showing 1-5 of 5 results.

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

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