A093850 - OEIS

%I #23 Sep 08 2022 08:45:13

%S 4,39,69,324,549,774,2799,4599,6399,8199,24999,39999,54999,69999,

%T 84999,228570,357141,485712,614283,742854,871425,2124999,3249999,

%U 4374999,5499999,6624999,7749999,8874999,19999999,29999999,39999999,49999999,59999999,69999999,79999999,89999999

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

%C 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.

%C 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.

%C 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

%H G. C. Greubel, <a href="/A093850/b093850.txt">Rows n = 1..100 of triangle, flattened</a>

%e Triangle begins with:

%e       4;

%e      39,    69;

%e     324,   549,   774;

%e    2799,  4599,  6399,  8199;

%e   24999, 39999, 54999, 69999, 84999;

%e   ....

%p A093850 := proc(n,r)

%p         10^(n-1)-1+r*floor(9*10^(n-1)/(n+1)) ;

%p end proc:

%p seq(seq(A093850(n,r),r=1..n),n=1..14) ; # _R. J. Mathar_, Sep 28 2011

%t Table[# -1 +r*Floor[9*#/(n+1)] &[10^(n-1)], {n, 8}, {r, n}]//Flatten (* _Michael De Vlieger_, Jul 18 2016 *)

%o (PARI) {T(n,k) = 10^(n-1) -1 +k*floor(9*10^(n-1)/(n+1))}; \\ _G. C. Greubel_, Mar 21 2019

%o (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

%o (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

%Y Cf. A093846, A093847, A061772, A093451, A093552.

%Y Cf. A093852.

%K easy,nonn,tabl,base

%O 1,1

%A _Amarnath Murthy_, Apr 18 2004

%E Second comment clarified by _Michael De Vlieger_, Jul 18 2016

%E Edited by _G. C. Greubel_, Mar 21 2019