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
a(7) = 510510 = 714*715 has prime divisors 2, 3, 5, 7, 11, 13 and 17.
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
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.
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[10^(n-1) -1 +n*Floor(9*10^(n-1)/(n+1)): n in [1..25]]; // G. C. Greubel, Mar 21 2019
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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
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Table[10^(n-1) -1 +n*Floor[9*10^(n-1)/(n+1)], {n,25}] (* G. C. Greubel, Mar 21 2019 *)
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{a(n) = 10^(n-1) -1 +n*floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Mar 21 2019
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[10^(n-1) -1 +n*floor(9*10^(n-1)/(n+1)) for n in (1..25)] # G. C. Greubel, Mar 21 2019
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
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.
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[10^(n-1) -1 +Floor(9*10^(n-1)/(n+1)): n in [1..20]]; // G. C. Greubel, Apr 02 2019
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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
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Table[10^(n-1) -1 +Floor[9*10^(n-1)/(n+1)], {n, 1, 20}] (* G. C. Greubel, Apr 02 2019 *)
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{a(n) = 10^(n-1) -1 +floor(9*10^(n-1)/(n+1))}; \\ G. C. Greubel, Apr 02 2019
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[10^(n-1) -1 +floor(9*10^(n-1)/(n+1)) for n in (1..20)] # G. C. Greubel, Apr 02 2019
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