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.

A088250 a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.

Original entry on oeis.org

1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870
Offset: 1

Views

Author

Amarnath Murthy, Sep 26 2003

Keywords

Comments

Conjectures: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.
Both conjectures follow from Dickson's conjecture. [Charles R Greathouse IV, Mar 14 2011]

Examples

			a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Mar 31 2017 *)

Extensions

Edited by Don Reble, Sep 29 2003
Entry revised by N. J. A. Sloane, Jan 05 2007
a(14) from Giovanni Resta, Mar 31 2017

A088651 a(n) = smallest number k such that rk-1 is prime for all r = 1 to n.

Original entry on oeis.org

3, 3, 4, 6, 6, 154770, 2894220, 2894220, 407874180, 214580145780, 9448481062020, 247236503934420, 2545206711847800, 18178612369988250180, 53792264108455702830
Offset: 1

Views

Author

Amarnath Murthy, Oct 29 2003

Keywords

Comments

Is the sequence finite?

Examples

			a(5)=6 because 1*6-1, 2*6-1, 3*6-1, 4*6-1, 5*6-1 are all prime.
a(11)=9448481062020 because all eleven numbers 1*9448481062020-1, 2*9448481062020-1,3*9448481062020-1,...,10*9448481062020-1 & 11*9448481062020-1 are prime and 9448481062020 is the smallest number with such property.
		

Crossrefs

Extensions

Corrected and extended by Ray Chandler, Nov 01 2003
More terms from Don Reble, Nov 23 2003
Entry revised by N. J. A. Sloane, Jan 05 2007
a(14)-a(15) from Jens Kruse Andersen, May 02 2008

A125839 a(n) is the smallest number m such that k*m - 1 is prime for all k=3,4,...,n.

Original entry on oeis.org

1, 1, 6, 18, 120, 1260, 1485540, 28667100, 28667100, 842889105240, 2281585556250, 163881570370980, 45187548280664790
Offset: 3

Views

Author

Luke Pebody (luke.pebody(AT)gmail.com), Jan 02 2007

Keywords

Comments

For n > 6, 10 divides a(n).

Examples

			a(11)=28667100 because 3*28667100-1, 4*28667100-1, 5*28667100-1, 6*28667100-1, 7*28667100-1, 8*28667100-1, 9*28667100-1, 10*28667100-1 & 11*28667100-1 are prime and 28667100 is the smallest number with this property.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := Block[{k = If[n<5, 1, 6], s}, s = k;  While[! AllTrue[k Range[3, n] - 1, PrimeQ], k += s]; k]; a /@ Range[3, 9] (* Giovanni Resta, Mar 29 2017 *)

Extensions

a(12)-a(13) from Farideh Firoozbakht
a(14)-a(15) from Giovanni Resta, Mar 30 2017

A164325 a(n) is the smallest number m such that (2k-1)m+1 is prime for all 0

Original entry on oeis.org

1, 2, 2, 6, 1170, 64590, 25153800, 25153800, 4747505070, 207187349040, 6703860240000, 26997529639080, 1760354281625940, 1760354281625940, 10718654377787155800
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 15 2009

Keywords

Crossrefs

Extensions

a(5) corrected by Zak Seidov, Sep 16 2009
a(10) and a(11) from Zak Seidov, Sep 17 2009
a(12)=26997529639080 from Zak Seidov, Sep 25 2009
a(13)-a(15) from Giovanni Resta, Apr 01 2017
Showing 1-4 of 4 results.