A076370 a(n) is the smallest number k such that primorial(k)^2 > primorial(n).

1, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41, 42, 43, 43, 44

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Example

For n = 7, primorial(7) = 2*3*5*7*11*13*17 = 510510;
  primorial(4)^2 = (2*3*5*7)^2 = 210^2 = 44100 < 510510
but
  primorial(5)^2 = (2*3*5*7*11)^2 = 2310^2 = 5336100 > 510510
so a(7) = 5.

Maple

p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
a:= proc(n) option remember; local k; for k from
      `if`(n=0, 0, a(n-1)) while p(k)^2<=p(n) do od; k
    end:
seq(a(n), n=0..74);  # Alois P. Heinz, Jul 20 2024

Mathematica

q[x_] := Apply[Times, Table[Prime[j], {j, 1, x}]] Table[Min[Flatten[Position[Table[Sign [q[j]-q[m]/q[j]], {j, 1, m}], 1]]], {m, 1, 250}]

Crossrefs

Cf. A002110.

Sequence in context: A308754 A339187 A309430 * A112318 A367069 A078489

Adjacent sequences: A076367 A076368 A076369 * A076371 A076372 A076373

Keyword

nonn,changed

Author

Labos Elemer, Oct 14 2002

Extensions

Edited by Jon E. Schoenfield, Jul 20 2024

a(0)=1 prepended by Alois P. Heinz, Jul 20 2024

Status

approved