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.

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A101174 Triangle formed by grouping the natural numbers so that the n-th row contains n numbers whose product has exactly n prime divisors, minimizing (1) final term of row and (2) product of terms of row.

Original entry on oeis.org

2, 3, 4, 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 48, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72
Offset: 1

Views

Author

Ray Chandler, Dec 03 2004

Keywords

Comments

Variation of A077172.

Examples

			Triangle begins:
2
3,4
1,5,6
7,8,9,10
11,12,13,14,16
15,17,18,19,20,21
22,23,24,25,26,27,28
29,30,31,32,33,34,35,36
37,38,39,40,41,42,43,45,48
44,46,47,49,50,51,52,53,54,55
56,57,58,59,60,61,62,63,64,65,66
67,68,69,70,71,72,73,74,75,76,77,80
78,79,81,82,83,84,85,86,87,88,89,90,91
		

Crossrefs

A093850 Triangle T(n,k) = 10^(n-1) -1 + k*floor(9*10^(n-1)/(n+1)), with 1 <= r <= n, read by rows.

Original entry on oeis.org

4, 39, 69, 324, 549, 774, 2799, 4599, 6399, 8199, 24999, 39999, 54999, 69999, 84999, 228570, 357141, 485712, 614283, 742854, 871425, 2124999, 3249999, 4374999, 5499999, 6624999, 7749999, 8874999, 19999999, 29999999, 39999999, 49999999, 59999999, 69999999, 79999999, 89999999
Offset: 1

Views

Author

Amarnath Murthy, Apr 18 2004

Keywords

Comments

The n-th row of this 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.
Starting with n=2, the n-th row of this triangle can be obtained by deleting the least significant digit, 9, from terms ending in 9 in the (n+1)-th row, and ignoring the main diagonal terms, of the triangle in A093846.
Floor(A093846(4,1)/10) = T(3,1) = 324, but floor(A093846(2,1)/10) = 5 and T(1,1) = 4, floor(A093846(7,1)/10) = 228571 and T(6,1) = 228570, etc. - Michael De Vlieger, Jul 18 2016

Examples

			Triangle begins with:
      4;
     39,    69;
    324,   549,   774;
   2799,  4599,  6399,  8199;
  24999, 39999, 54999, 69999, 84999;
  ....
		

Crossrefs

Programs

  • Magma
    [[10^(n-1) -1 +k*Floor(9*10^(n-1)/(n+1)): k in [1..n]]: n in [1..8]]; // G. C. Greubel, Mar 21 2019
    
  • Maple
    A093850 := proc(n,r)
            10^(n-1)-1+r*floor(9*10^(n-1)/(n+1)) ;
    end proc:
    seq(seq(A093850(n,r),r=1..n),n=1..14) ; # R. J. Mathar, Sep 28 2011
  • Mathematica
    Table[# -1 +r*Floor[9*#/(n+1)] &[10^(n-1)], {n, 8}, {r, n}]//Flatten (* Michael De Vlieger, Jul 18 2016 *)
  • PARI
    {T(n,k) = 10^(n-1) -1 +k*floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Mar 21 2019
    
  • Sage
    [[10^(n-1) -1 +k*floor(9*10^(n-1)/(n+1)) for k in (1..n)] for n in (1..8)] # G. C. Greubel, Mar 21 2019

Extensions

Second comment clarified by Michael De Vlieger, Jul 18 2016
Edited by G. C. Greubel, Mar 21 2019
Showing 1-2 of 2 results.