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.

User: Jon Grantham

Jon Grantham's wiki page.

Jon Grantham has authored 2 sequences.

A033501 Almost-squares: m such that m/p(m) >= k/p(k) for all k

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 24, 25, 28, 30, 35, 36, 40, 42, 48, 49, 54, 56, 60, 63, 64, 70, 72, 77, 80, 81, 88, 90, 96, 99, 100, 108, 110, 117, 120, 121, 130, 132, 140, 143, 144, 150, 154, 156, 165, 168, 169, 176, 180, 182, 192, 195, 196, 204, 208, 210
Offset: 1

Author

Greg Martin; suggested by Jon Grantham

Keywords

Comments

Also integers that can be written in the form k*(k+h), for some integers k>=1 and 0 <= h <= T(k), where T(x) is the number of triangular numbers binomial(x+1,2) not exceeding x. (Corollary 1 in Greg Martin's article) - Hugo Pfoertner, Sep 23 2017

Crossrefs

Cf. A000217.

Programs

  • Mathematica
    chs={1}; For[ n=2, n<=99, n++, chs=Join[ chs, Reverse[ Table[ (n-1-i)(n+i), {i, 0, (Sqrt[ 2n-1 ]-1)/2} ] ], Reverse[ Table[ (n-i)(n+i), {i, 0, n/Sqrt[ 2n-1 ]} ] ] ] ]
    (*code uses alternate characterization, lists almost-squares up to 99^2*)

A018188 The $620 prime list.

Original entry on oeis.org

5003, 5987, 6563, 9803, 10427, 11027, 11867, 16763, 19403, 22283, 22907, 24923, 25667, 29867, 35747, 40427, 40763, 41243, 42083, 49307, 54323, 54347, 57203, 57347, 66587, 67307, 73883, 78203, 84347, 104003, 112067, 121403
Offset: 1

Author

N. J. A. Sloane, Jon Grantham (grantham(AT)math.uga.edu)

Keywords

Comments

Numbers are 11 mod 24.
Jon Grantham: "I strongly believe that some sub-product of these primes is a Carmichael number and a Lucas pseudoprime for the Fibonacci sequence, and also is 2 or 3 mod 5."
In particular the above conjecture implies that there is a BPSW pseudoprime smaller than 10^25286. - Charles R Greathouse IV, Sep 28 2019

Crossrefs

Subsequence of A107007 (and hence A000040).

Extensions

b-file from Charles R Greathouse IV, Aug 28 2010