OFFSET
1,1
COMMENTS
A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
EXAMPLE
The terms together with their binary expansions and binary indices begin:
8: 1000 ~ {4}
32: 100000 ~ {6}
40: 101000 ~ {4,6}
256: 100000000 ~ {9}
264: 100001000 ~ {4,9}
288: 100100000 ~ {6,9}
296: 100101000 ~ {4,6,9}
512: 1000000000 ~ {10}
520: 1000001000 ~ {4,10}
544: 1000100000 ~ {6,10}
552: 1000101000 ~ {4,6,10}
768: 1100000000 ~ {9,10}
776: 1100001000 ~ {4,9,10}
800: 1100100000 ~ {6,9,10}
808: 1100101000 ~ {4,6,9,10}
MATHEMATICA
bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
semi[n_]:=PrimeOmega[n]==2;
Select[Range[10000], And@@semi/@bix[#]&]
PROG
(Python)
from math import isqrt
from sympy import primepi, primerange
def A371454(n):
def f(x, n): return int(n+x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//k) for k in primerange(1, s+1)))
def A001358(n):
m, k = n, f(n, n)
while m != k:
m, k = k, f(k, n)
return m
return sum(1<<A001358(i)-1 for i, j in enumerate(bin(n)[:1:-1], 1) if j=='1') # Chai Wah Wu, Aug 16 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Apr 02 2024
STATUS
approved