A379036 Indices of zeros in binary concatenation of primes.

1, 5, 11, 16, 19, 20, 21, 24, 25, 29, 36, 44, 45, 47, 50, 52, 53, 56, 58, 62, 69, 71, 76, 83, 86, 87, 88, 89, 93, 94, 95, 100, 101, 103, 104, 107, 108, 114, 116, 117, 121, 124, 125, 129, 130, 131, 132, 136, 137, 139, 143, 144, 150, 152, 157, 160, 165, 166, 167

Offset: 1

Author

Alexandre Herrera, Dec 14 2024

Keywords

• nonn
• base

Comments

The initial bit is labeled as bit 0.

Examples

			The primes, their binary expansions, and positions of successive zero bits, begin
   prime    2  3   5   7   11 ...
   binary  10 11 101 111 1011 ...
   zeros    ^     ^       ^
   a(n) =   1     5      11   ...
		

Crossrefs

Cf. A003607, A191232.

Programs

Mathematica

seq[lim_] := -1 + Position[Flatten@ IntegerDigits[Prime[Range[lim]], 2], 0] // Flatten; seq[30] (* Amiram Eldar, Dec 31 2024 *)

Python

import sympy
l = []
bin_primes = ""
for i in range(1,27):
    bin_primes += bin(sympy.prime(i))[2:]
for i in range(len(bin_primes)):
    if bin_primes[i] == '0':
        l.append(i)
print(l)