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.

A144851 a(n) = number of distinct prime divisors (taken together) of numbers of the form 2x^2+1 for x<=10^n.

Original entry on oeis.org

8, 76, 760, 7445, 73477, 726948, 7218256, 71801859, 715087632, 7127665635, 71089166879, 709344259821
Offset: 1

Views

Author

Artur Jasinski & Bernhard Helmes (bhelmes(AT)gmx.de), Sep 22 2008

Keywords

Links

Crossrefs

Cf. A002383, A143835, A143868, A144848, A144850.

Programs

  • Mathematica
    d = 10; l = 0; p = 2; c = {}; a = {}; Do[k = p x^2 + 1; b = Divisors[k]; Do[If[PrimeQ[b[[n]]], AppendTo[a, b[[n]]]], {n, 1, Length[b]}]; If[x == d, a = Union[a]; l = Length[a]; d = 10 d; Print[l]; AppendTo[c, l]], {x, 1, 10000}]; c (*Artur Jasinski*)

Extensions

Fixed broken link, corrected and extended to agree with website. - Ray Chandler, Jun 30 2015

A144850 a(n) = number of distinct prime divisors (taken together) of numbers of the form x^2+x+1 for x<=10^n.

Original entry on oeis.org

8, 74, 734, 7233, 71653, 712026, 7090655, 70686855, 705173825, 7038475146, 70278276834, 701910715473
Offset: 1

Views

Author

Artur Jasinski & Bernhard Helmes (bhelmes(AT)gmx.de), Sep 22 2008

Keywords

Links

Crossrefs

Cf. A002383, A143835, A143868, A144848, A144851.

Programs

  • Mathematica
    d = 10; l = 0; p = 1; c = {}; a = {}; Do[k = p x^2 + x + 1; b = Divisors[k]; Do[If[PrimeQ[b[[n]]], AppendTo[a, b[[n]]]], {n, 1, Length[b]}]; If[x == d, a = Union[a]; l = Length[a]; d = 10 d; Print[l]; AppendTo[c, l]], {x, 1, 10000}]; c (*Artur Jasinski*)

Extensions

Fixed broken link, corrected and extended to agree with website. - Ray Chandler, Jun 30 2015

A144852 a(n) = number of distinct prime divisors (taken together) of numbers of the form 4x^2+1 for x<=10^n.

Original entry on oeis.org

9, 87, 836, 8000, 78124, 766585, 7556731, 74771106, 741554656, 7366252759, 73261462211, 729280694469
Offset: 1

Views

Author

Artur Jasinski & Bernhard Helmes (bhelmes(AT)gmx.de), Sep 22 2008

Keywords

Comments

Primes of the form 4x^2+1 see A121326(n) = A002496(n+1).

Links

Crossrefs

Cf. A002383, A121326, A143835, A143868, A144848, A144850, A144851.

Programs

  • Mathematica
    d = 10; l = 0; p = 4; c = {}; a = {}; Do[k = p x^2 + 1; b = Divisors[k]; Do[If[PrimeQ[b[[n]]], AppendTo[a, b[[n]]]], {n, 1, Length[b]}]; If[x == d, a = Union[a]; l = Length[a]; d = 10 d; Print[l]; AppendTo[c, l]], {x, 1, 10000}]; c (*Artur Jasinski*)

Extensions

Fixed broken link, corrected and extended to agree with website. - Ray Chandler, Jun 30 2015

A144861 Primitive prime factors of the sequence 2k^2 - 1 in the order in which they are first found.

Original entry on oeis.org

7, 17, 31, 71, 97, 127, 23, 199, 241, 41, 337, 449, 73, 577, 647, 103, 47, 881, 967, 151, 1151, 1249, 193, 1567, 257, 113, 89, 311, 2311, 79, 2591, 2887, 3041, 457, 3361, 3527, 3697, 4049, 4231, 631, 271, 4801, 4999, 743, 5407, 137, 263, 6271, 6961, 313, 1063
Offset: 2

Views

Author

Bernhard Helmes (pi(AT)devalco.de), Sep 23 2008

Keywords

Comments

Every Mersenne prime number appears on this sequence. a(n) mod 8 = 1 or 7.

Links

Crossrefs

Cf. A005529, A144848.

Programs

  • Mathematica
    Rest[DeleteDuplicates[#[[1]]&/@(Flatten[FactorInteger/@(2*Range[100]^2-1),1])]] (* Harvey P. Dale, Nov 15 2014 *)

Extensions

Definition clarified by Harvey P. Dale, Nov 15 2014
Showing 1-4 of 4 results.

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

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