A119447 Leading diagonal of triangle A119446.

2, 2, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 13, 13, 7, 7, 7, 7, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19

Offset

1,1

Comments

a(181) = 27 is the first term greater than 19. This is because prime(181)/181 > 6 for the first time. In general this sequence is determined by prime(n)/n: the pattern for each row of the triangle is that it ends with prime(n), preceded by multiples of k = prime(n)/n down to k^2, then the largest multiple of k-1 less than k^2 and the largest multiple of k-2 less than that and so on. This sequence gives the multiple of 1. See A000960 for the sequence that gives the ending value for each starting k.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A000960( prime(n)/n ).

a(n) = A119446(n, n).

Mathematica

t[1, n_]:= Prime[n];
t[m_, n_]/; 1<m<=n:= t[m, n]= (n-m+1)*Floor[(t[m-1, n]-1)/(n-m+1)];
t[_, _]=0;
A119447[n_]:= A119447[n]= t[n, n];
Table[A119447[n], {n, 100}] (* G. C. Greubel, Apr 07 2023 *)

Prog

(Magma)
function t(n, k) // t = A119446
  if k eq 1 then return NthPrime(n);
  else return (n-k+1)*Floor((t(n, k-1) -1)/(n-k+1));
  end if;
end function;
[t(n, n): n in [1..100]]; // G. C. Greubel, Apr 07 2023
(SageMath)
def t(n, k): # t = A119446
    if (k==1): return nth_prime(n)
    else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
def A119447(n): return t(n, n)
[A119447(n) for n in range(1, 101)] # G. C. Greubel, Apr 07 2023

Crossrefs

Cf. A000960, A119444, A119446.

Sequence in context: A345377 A096143 A025792 * A157720 A077463 A084556

Adjacent sequences: A119444 A119445 A119446 * A119448 A119449 A119450

Keyword

nonn

Author

Joshua Zucker, May 20 2006

Status

approved