A309399 Number of lucky numbers l between powers of 2, 2^n < l <= 2^(n+1).

0, 1, 1, 3, 3, 6, 12, 21, 38, 71, 123, 234, 427, 791, 1477, 2774, 5222, 9849, 18659, 35412, 67410, 128644, 245959, 471166, 904186, 1738238, 3346542, 6452030, 12455921, 24076458, 46591766, 90258683, 175029533

Offset: 0

Author

Hauke Löffler, Jul 28 2019

Keywords

• nonn
• more

Examples

			a(0) = 0 because there are no lucky numbers between 1 (2^0) and 2 (2^1).
a(3) = 3 because there are 3 lucky numbers (9, 13, 15) between 8 (2^3) and 16 (2^4).
		

Crossrefs

Cf. A000959, A036378.

Programs

SageMath

def lucky(n):
  L=list(range(1, n+1, 2)); j=1
  while L[j] <= len(L)-1:
    L=[L[i] for i in range(len(L)) if (i+1)%L[j]!=0]
    j+=1
  return(L)
A000959=lucky(1048576)
def lucky_range(a, b):
    lucky = []
    for l in A000959:
        if l >= b:
            return lucky
        if l>=a: lucky.append(l)
[ len(lucky_range((2^n)+1,2^(n+1))) for n in range(19)]

Extensions

a(19)-a(30) from Giovanni Resta, May 10 2020

a(31)-a(32) from Kevin P. Thompson, Nov 22 2021