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.

A083203 a(1) = 1, then smallest number not included earlier such that a(n)*a(n+1) + 1 is a cube.

Original entry on oeis.org

1, 7, 9, 38, 35, 117, 91, 8, 614, 39312, 167143, 9225632, 27823518, 3438671571811, 810534219404852834, 350099109163999874259659131507909, 538073411436415103320989698699207584507533583587852139
Offset: 1

Views

Author

Amarnath Murthy, Apr 28 2003

Keywords

Comments

The next 3 terms are (to 2 significant digits) 4.1*10^95, 1.3*10^183, 3.6*10^351.

Examples

			7*9 + 1 = 64 = 8^3, 9*38 + 1 = 343= 7^3.

Crossrefs

Cf. A083204, A082536.
Cf. A091569.

Extensions

Corrected and extended by Vladeta Jovovic, May 01 2003
More terms from Michel ten Voorde Jun 23 2003
More terms from Vladeta Jovovic, Jun 29 2003
a(15) - a(17) from David Wasserman, Mar 18 2004
More terms from David Wasserman, May 20 2004

A082537 Cubes arising in A082536.

Original entry on oeis.org

2, 4, 7, 39, 183, 269, 297, 3665, 924109, 4033584664, 189735334108567843, 143328637617784835849199812569, 120097694647175196504595164577946008733316783100605
Offset: 1

Views

Author

Amarnath Murthy, Apr 28 2003

Keywords

Crossrefs

Cf. A082536, A083204.

Formula

a(n) = (A082536(n)*A082536(n+1)+1)^(1/3) - David Wasserman, May 27 2004

Extensions

Corrected and extended by Vladeta Jovovic, May 01 2003
More terms from Michel ten Voorde Jun 23 2003
More terms from David Wasserman, May 27 2004

A083205 a(1) = 1, then smallest number not included earlier such that a(n)*a(n+1) + 1 is an n-th power.

Original entry on oeis.org

1, 2, 4, 31, 26129, 466202136816810031, 10584868011442581563053546190350068005080430521324963528734180259722815036145
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 28 2003

Keywords

Comments

The sequence is infinite and a(n+1) <= ([a(n)+1]^n - 1)/a(n) when n is even, or a(n+1) <= ([a(n)-1]^n - 1)/a(n) when n is odd.
To find a(6), we need an x such that x^5 = 1 (mod a(5)); then a(6) = (x^5 - 1)/a(5). The multiplicative group mod a(5) has order phi(a(5)) = 23296, which is not divisible by 5. So the only 5th root of 1 in this group is 1. x = 1 would give a(6) = 0, this is not allowed, so we take x to be the next representative of 1 mod a(5), i.e. a(5)+1. So a(6) = [(a(5)+1)^5 - 1]/a(5). - David Wasserman, Mar 02 2004
Next term is approximately 8.1*10^451. - David Wasserman, May 26 2004

Examples

			a(4) = 31, a(5) = 26129, 31*26129 + 1 = 810000 = 30^4.

Crossrefs

Cf. A083203, A083204.

Extensions

More terms from David Wasserman, Mar 02 2004

A082606 n-th powers arising in A082605.

Original entry on oeis.org

3, 9, 125, 810000, 12181395632886429300000
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 28 2003

Keywords

Comments

The sequence is infinite.

Crossrefs

Cf. A083203, A083204, A083205.

Formula

a(n) = A083205(n)*A083205(n+1)+1. - David Wasserman, Sep 21 2004

Extensions

More terms from David Wasserman, Sep 21 2004
Showing 1-4 of 4 results.

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

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