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.

A093449 Least number with n distinct prime divisors arising as the product of two or more consecutive integers.

Original entry on oeis.org

2, 6, 30, 210, 2730, 39270, 510510, 23393370, 363993630, 64790866140, 530514844860, 126408523110870, 3425113062060690, 660393717163700520, 26657280574571657010, 3448055881024876471350, 308480161111936386482910
Offset: 1

Views

Author

Amarnath Murthy, Apr 03 2004

Keywords

Comments

2, 6, 30, 210 and 510510 are primorials (A002110). There are no more primorials in the first 300 terms.
Upper bounds for a(14)-a(18): 660393717163700520, 28386773771493397260, 3448055881024876471350, 308480161111936386482910, 32521466098360753728404190.

Examples

			a(7) = 510510 = 714*715 has prime divisors 2, 3, 5, 7, 11, 13 and 17.
		

Crossrefs

Extensions

Edited, corrected and extended by David Wasserman, Mar 21 2007
a(14)-a(17) from Donovan Johnson, Sep 13 2008

A093852 a(n) = 10^(n-1) - 1 + n*floor(9*10^(n-1)/(n+1)).

Original entry on oeis.org

4, 69, 774, 8199, 84999, 871425, 8874999, 89999999, 909999999, 9181818179, 92499999999, 930769230759, 9357142857140, 93999999999999, 943749999999999, 9470588235294111, 94999999999999999, 952631578947368403, 9549999999999999999, 95714285714285714279
Offset: 1

Views

Author

Amarnath Murthy, Apr 18 2004

Keywords

Comments

This sequence is the main diagonal of A093850.

Examples

			n-th row of the following triangle contains n uniformly located n-digit numbers. i.e. n terms of an arithmetic progression with 10^(n-1)-1 as the term preceding the first term and (n+1)-th term is the largest possible n-digit term.
Given the triangle defined in A093850:
...4;
..39   69;
.324  549  774;
2799 4599 6399 8199.....
then this sequence is the leading diagonal.
		

Crossrefs

Programs

  • Magma
    [10^(n-1) -1 +n*Floor(9*10^(n-1)/(n+1)): n in [1..25]]; // G. C. Greubel, Mar 21 2019
    
  • Maple
    A093852 := proc(n)
            r := n ;
            10^(n-1)-1+r*floor(9*10^(n-1)/(n+1)) ;
    end proc:
    seq(A093852(n),n=1..50) ; # R. J. Mathar, Oct 01 2011
  • Mathematica
    Table[10^(n-1) -1 +n*Floor[9*10^(n-1)/(n+1)], {n,25}] (* G. C. Greubel, Mar 21 2019 *)
  • PARI
    {a(n) = 10^(n-1) -1 +n*floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Mar 21 2019
    
  • Sage
    [10^(n-1) -1 +n*floor(9*10^(n-1)/(n+1)) for n in (1..25)] # G. C. Greubel, Mar 21 2019

A093851 a(n) = A002283(n-1) + floor(A052268(n)/(1+n)).

Original entry on oeis.org

4, 39, 324, 2799, 24999, 228570, 2124999, 19999999, 189999999, 1818181817, 17499999999, 169230769229, 1642857142856, 15999999999999, 156249999999999, 1529411764705881, 14999999999999999, 147368421052631577, 1449999999999999999, 14285714285714285713
Offset: 1

Views

Author

Amarnath Murthy, Apr 18 2004

Keywords

Comments

The first column r=1 of a triangle defined by T(n,r) = 10^(n-1) -1 + r*floor(9*10^(n-1)/(n+1)).
A row starts with a (virtual) 0th column of a rep-9-digit and fills the remainder with n+1 numbers in arithmetic progression with the largest step such that all numbers in the n-th row are n-digit numbers.

Examples

			The triangle starts in row n=1 as
4 9 # -1, -1+5, -1+2*5
39 69 99 # 9,9+30,9+2*30
324 549 774 999 # 99, 99+225, 99+2*225, 99+3*225
2799 4599 6399 8199 9999 # 999, 999+1800, 999+2*1800,..
...
The sequence contains the first column.
		

Crossrefs

Programs

  • Magma
    [10^(n-1) -1 +Floor(9*10^(n-1)/(n+1)): n in [1..20]]; // G. C. Greubel, Apr 02 2019
    
  • Maple
    A093851 := proc(n) 10^(n-1)-1+floor(9*10^(n-1)/(n+1)) ; end proc: seq(A093851(n),n=1..20) ; # R. J. Mathar, Oct 14 2010
  • Mathematica
    Table[10^(n-1) -1 +Floor[9*10^(n-1)/(n+1)], {n, 1, 20}] (* G. C. Greubel, Apr 02 2019 *)
  • PARI
    {a(n) = 10^(n-1) -1 +floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Apr 02 2019
    
  • Sage
    [10^(n-1) -1 +floor(9*10^(n-1)/(n+1)) for n in (1..20)] # G. C. Greubel, Apr 02 2019

Formula

a(n) = 10^(n-1) -1 + floor(9*10^(n-1)/(n+1)). - G. C. Greubel, Apr 02 2019

Extensions

More terms from R. J. Mathar, Oct 14 2010
Showing 1-3 of 3 results.