A309399 - OEIS

%I #17 Aug 07 2023 03:55:34

%S 0,1,1,3,3,6,12,21,38,71,123,234,427,791,1477,2774,5222,9849,18659,

%T 35412,67410,128644,245959,471166,904186,1738238,3346542,6452030,

%U 12455921,24076458,46591766,90258683,175029533

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

%e a(0) = 0 because there are no lucky numbers between 1 (2^0) and 2 (2^1).

%e a(3) = 3 because there are 3 lucky numbers (9, 13, 15) between 8 (2^3) and 16 (2^4).

%o (SageMath)

%o def lucky(n):

%o   L=list(range(1, n+1, 2)); j=1

%o   while L[j] <= len(L)-1:

%o     L=[L[i] for i in range(len(L)) if (i+1)%L[j]!=0]

%o     j+=1

%o   return(L)

%o A000959=lucky(1048576)

%o def lucky_range(a, b):

%o     lucky = []

%o     for l in A000959:

%o         if l >= b:

%o             return lucky

%o         if l>=a: lucky.append(l)

%o [ len(lucky_range((2^n)+1,2^(n+1))) for n in range(19)]

%Y Cf. A000959, A036378.

%K nonn,more

%O 0,4

%A _Hauke Löffler_, Jul 28 2019

%E a(19)-a(30) from _Giovanni Resta_, May 10 2020

%E a(31)-a(32) from _Kevin P. Thompson_, Nov 22 2021