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A093850 Triangle T(n,k) = 10^(n-1) -1 + k*floor(9*10^(n-1)/(n+1)), with 1 <= r <= n, read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
EXAMPLE
Triangle begins with:
4;
39, 69;
324, 549, 774;
2799, 4599, 6399, 8199;
24999, 39999, 54999, 69999, 84999;
....
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 *)
PROG
(PARI) {T(n, k) = 10^(n-1) -1 +k*floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Mar 21 2019
(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
(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
CROSSREFS
Cf. A093852.
Sequence in context: A018860 A016484 A278052 * A297736 A286359 A201740
KEYWORD
easy,nonn,tabl,base
AUTHOR
Amarnath Murthy, Apr 18 2004
EXTENSIONS
Second comment clarified by Michael De Vlieger, Jul 18 2016
Edited by G. C. Greubel, Mar 21 2019
STATUS
approved

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)