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 1-3 of 3 results.

A079581 Consider pairs (r,s) such that the polynomial (x^r+1) divides (x^s+1) and 1 <= r < s. This sequence gives the s values; A079673 gives the r values.

Original entry on oeis.org

3, 5, 6, 7, 9, 9, 10, 11, 12, 13, 14, 15, 15, 15, 17, 18, 18, 19, 20, 21, 21, 21, 22, 23, 24, 25, 25, 26, 27, 27, 27, 28, 29, 30, 30, 30, 31, 33, 33, 33, 34, 35, 35, 35, 36, 36, 37, 38, 39, 39, 39, 40, 41, 42, 42, 42, 43, 44, 45, 45, 45, 45, 45, 46, 47, 48, 49, 49, 50, 50, 51
Offset: 1

Views

Author

Jose R. Brox (tautocrona(AT)terra.es), Jan 25 2003

Keywords

Comments

(x^r+1) divides (x^s+1) iff s/r is an odd integer.

Examples

			9 is in the sequence twice because (x^1+1) and (x^3+1) divide (x^9+1).

Crossrefs

Cf. A079665, A079672, A079673.

Extensions

Edited by Don Reble, Jun 12 2003

A079665 Triangular array read by rows: row s contains integers of the form (2^s+1)/(2^r+1) in order of increasing r <= s-1.

Original entry on oeis.org

3, 11, 13, 43, 171, 57, 205, 683, 241, 2731, 3277, 10923, 3641, 993, 43691, 52429, 4033, 174763, 61681, 699051, 233017, 16257, 838861, 2796203, 65281, 11184811, 1016801, 13421773, 44739243, 14913081, 261633, 15790321, 178956971, 214748365
Offset: 1

Views

Author

Jose R. Brox (tautocrona(AT)terra.es), Jan 25 2003

Keywords

Comments

Conjecture: (b^s+1)/(b^r+1) is an integer if and only if: 1) r

Examples

			s=2: no terms
s=3: 3
s=4: no terms
s=5: 11
s=6: 13
s=7: 43
s=8: no terms
s=9: 171, 57
...

Crossrefs

Cf. A079672, A079581, A079673, A370425.

Programs

  • PARI
    for(x=2,30, for(y=1,x-1,if(Mod(2^x+1,2^y+1),0,print1((2^x+1)\(2^y+1)","))))

Extensions

Definition corrected by Max Alekseyev, Feb 18 2024

A079672 Numbers of the form (3^s+1)/(3^r+1) for s > 1, 1 <= r <= s-1.

Original entry on oeis.org

7, 61, 73, 547, 4921, 703, 5905, 44287, 6481, 398581, 478297, 3587227, 512461, 58807, 32285041, 38742049, 530713, 290565367, 42521761, 2615088301, 373584043, 4780783, 3138105961, 23535794707, 43040161, 211822152361, 3472494301
Offset: 1

Views

Author

Jose R. Brox (tautocrona(AT)terra.es), Jan 25 2003

Keywords

Comments

(b^s+1) / (b^r+1) is an integer iff s/r is odd. - Jose Brox (tautocrona(AT)terra.es), Dec 27 2005

Crossrefs

Cf. A079665, A079581, A079673.

Programs

  • PARI
    for(x=2,26, for(y=1,x-1,if(Mod(2^x+1,2^y+1),0,print1((3^x+1)/(3^y+1)",")))) \\ The Mod(2^x+1,2^y+1) is not a bug, since the exponents do not depend on the base in which they are calculated.
Showing 1-3 of 3 results.

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

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