A360448 Indices of primes of the form p = 2^i + 2^j + 1, i > j > 0 (A081091).

4, 5, 6, 8, 12, 13, 19, 21, 25, 32, 33, 44, 98, 106, 116, 136, 174, 191, 310, 313, 319, 565, 568, 1029, 1470, 1902, 2111, 3513, 3518, 3521, 4289, 6544, 12426, 13632, 15000, 23001, 23003, 23043, 23673, 43395, 43420, 43465, 45859, 62947, 82029, 82063, 91466, 155612, 155900, 295957, 564164

Offset

1,1

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = A000720(A081091(n)).

This sequence = { n | A000120(A000040(n)) = 3 }.

Mathematica

Position[Prime[Range[600000]], _?(DigitCount[#, 2, 1] == 3 &)] // Flatten (* Amiram Eldar, Mar 04 2023 *)
PrimePi@ Union@ Select[Flatten@ Table[2^i + 2^j + 1, {i, 0, 23}, {j, 0, i - 1}], PrimeQ] (* Michael De Vlieger, Mar 21 2023 *)

Prog

(PARI) A360448(n) = primepi(A081091(n))
is_A360448(n) = hammingweight(prime(n))==3
(Python)
from itertools import count, islice
from sympy import primepi, isprime
def A360448_gen(): # generator of terms
    for i in count(2):
        k = (1<<i)+1
        for j in range(1, i):
            if isprime(m := k+(1<<j)):
                yield primepi(m)
A360448_list = list(islice(A360448_gen(), 20)) # Chai Wah Wu, Mar 21 2023

Crossrefs

Cf. A000720 (prime counting function), A081091 (primes of the form 2^i + 2^j + 1, i > j > 0), A014499 (Hamming weight of the n-th prime), A000040 (the primes), A000120 (Hamming weight).

Sequence in context: A030343 A030590 A047430 * A204098 A115838 A310572

Adjacent sequences: A360445 A360446 A360447 * A360449 A360450 A360451

Keyword

nonn

Author

M. F. Hasler, Mar 03 2023

Status

approved