A372402 Position of 2310^n among 11-smooth numbers A051038.

1, 283, 3847, 20996, 74228, 203084, 469053, 960396, 1797086, 3135610, 5173909, 8156188, 12377846, 18190320, 26005929, 36302854, 49629820, 66611231, 87951744, 114441450, 146960432, 186483973, 234087084, 290949702, 358361266, 437725888, 530566933, 638532124, 763398291, 907076258

Offset: 0

Author

Michael De Vlieger, Jun 03 2024

Keywords

• nonn

Comments

Also position of 2310^(n+1) in A147572.

Crossrefs

Cf. A022330, A051038, A147572, A372400, A372401.

Programs

Mathematica

Table[
  Sum[Floor@ Log[11, 2310^n/(2^i*3^j*5^k*7^m)] + 1,
    {i, 0, Log[2, 2310^n]},
    {j, 0, Log[3, 2310^n/2^i]},
    {k, 0, Log[5, 2310^n/(2^i*3^j)]},
    {m, 0, Log[7, 2310^n/(2^i*3^j*5^k)]}],
  {n, 0, 8}]

Python

# uses imports/function in A372401
print(list(islice(A372401gen(p=11), 7))) # Michael S. Branicky, Jun 05 2024

Python

from sympy import integer_log, prevprime
def A372402(n):
    def g(x,m): return sum((x//3**i).bit_length() for i in range(integer_log(x,3)[0]+1)) if m==3 else sum(g(x//(m**i),prevprime(m))for i in range(integer_log(x,m)[0]+1))
    return g(2310**n,11) # Chai Wah Wu, Sep 16 2024

Extensions

a(14)-a(18) from Michael S. Branicky, Jun 05 2024

More terms from David A. Corneth, Jun 05 2024