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

1,2

Comments

The initial bit is labeled as bit 0.

Links

Table of n, a(n) for n=1..59.

Example

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   ...

Mathematica

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

Prog

(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)

Crossrefs

Cf. A003607, A191232.

Sequence in context: A072557 A324076 A314081 * A314082 A314083 A314084

Adjacent sequences: A379033 A379034 A379035 * A379037 A379038 A379039

Keyword

nonn,base

Author

Alexandre Herrera, Dec 14 2024

Status

approved