A118752 -id:A118752 - cp's OEIS frontend

A118751 Smallest prime >= 3*n.

2, 5, 7, 11, 13, 17, 19, 23, 29, 29, 31, 37, 37, 41, 43, 47, 53, 53, 59, 59, 61, 67, 67, 71, 73, 79, 79, 83, 89, 89, 97, 97, 97, 101, 103, 107, 109, 113, 127, 127, 127, 127, 127, 131, 137, 137, 139, 149, 149, 149, 151, 157, 157, 163, 163, 167, 173, 173, 179, 179, 181

Offset: 0

Jonathan Vos Post, Apr 29 2006

Analogous to A060264 = first prime after 2n.

Cf. A060308, A060264, A118750, A118752.

A258566 Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order.

Original entry on oeis.org

1, 3, 2, 15, 10, 6, 105, 70, 42, 30, 1155, 770, 462, 330, 210, 15015, 10010, 6006, 4290, 2730, 2310, 255255, 170170, 102102, 72930, 46410, 39270, 30030, 4849845, 3233230, 1939938, 1385670, 881790, 746130, 570570, 510510

Offset: 1

Philippe Deléham, Jun 03 2015

Triangle read by rows, truncated rows of the array in A185973.

Reversal of A077011.

			Triangle begins:
      1;
      3,     2;
     15,    10,    6;
    105,    70,   42,   30;
   1155,   770,  462,  330,  210;
  15015, 10010, 6006, 4290, 2730, 2310;
  ...

Row sums: A024451.
T(n,1) = A070826(n).
T(n,n) = A002110(n-1).
For 2 <= n <= 9, T(n,2) = A118752(n-2). [corrected by Peter Munn, Jan 13 2018]
T(n,k) = A121281(n,k), but the latter has an extra column (0).
Cf. A077011, A185973, A286947.

T:= n-> (m-> seq(m/ithprime(j), j=1..n))(mul(ithprime(i), i=1..n)):
seq(T(n), n=1..10);  # Alois P. Heinz, Jun 18 2015

T[1, 1] = 1; T[n_, n_] := T[n, n] = Prime[n-1]*T[n-1, n-1];
T[n_, k_] := T[n, k] = Prime[n]*T[n-1, k];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, May 26 2016 *)

T(1,1) = 1, T(n,k) = A000040(n)*T(n-1,k) for k < n, T(n,n) = A000040(n-1) * T(n-1,n-1).

A118749 Largest prime <= 3*n.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 23, 29, 31, 31, 37, 41, 43, 47, 47, 53, 53, 59, 61, 61, 67, 71, 73, 73, 79, 83, 83, 89, 89, 89, 97, 101, 103, 107, 109, 113, 113, 113, 113, 113, 127, 131, 131, 137, 139, 139, 139, 149, 151, 151, 157, 157, 163, 167, 167, 173, 173, 179, 181

Offset: 1

Jonathan Vos Post, Apr 29 2006

Analogous to A060308 largest prime <= 2*k.

Cf. A007917 (largest prime <= n), A008585 (3n).
Cf. A060308, A118750, A118751, A118752.
Essentially the same as A081259.

[NthPrime(#PrimesUpTo(3*n)): n in [1..100]]; // Vincenzo Librandi, Nov 25 2015

Table[Max[FactorInteger[(3 n)!/(n!)^3]], {n, 1, 70}] (* Vincenzo Librandi, Nov 25 2015 *)
NextPrime[3*Range[70]+1,-1] (* Harvey P. Dale, Nov 12 2017 *)

vector(100, n, precprime(3*n)) \\ Altug Alkan, Nov 25 2015

a(n) = A007917(A008585(n)). - Michel Marcus, Nov 25 2015

cp's OEIS Frontend

A118751 Smallest prime >= 3*n.

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A258566 Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order.

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A118749 Largest prime <= 3*n.

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