A377897 Numbers k such that k + PrimePi(k) is even.

4, 5, 8, 10, 11, 14, 16, 17, 20, 22, 23, 25, 27, 30, 31, 33, 35, 38, 40, 41, 44, 46, 47, 49, 51, 54, 56, 58, 59, 62, 64, 66, 67, 69, 72, 73, 75, 77, 80, 82, 83, 85, 87, 90, 92, 94, 96, 97, 99, 102, 103, 105, 108, 109, 111, 114, 116, 118, 120, 122, 124, 126, 127, 129, 132, 134, 136, 137, 140

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[200], EvenQ[# + PrimePi[#]] &] (* Paolo Xausa, Nov 13 2024 *)

Prog

(Python)
from sympy import nextprime
def A377897_gen(): # generator of terms
    p, q, a = 3, 5, 1
    while True:
        yield from range(p+a, q, 2)
        p, q, a = q, nextprime(q), a^1
A377897_list = list(islice(A377897_gen(), 69)) # Chai Wah Wu, Nov 13 2024
(Python)
from sympy import primepi, prevprime
def A377897(n):
    def f(x):
        if x<=3: return n+x
        p = prevprime(x+1)
        i = int(primepi(p))
        return n+x-(p>>1)-(x-p-((i^x)&1)>>1)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Nov 13 2024

Crossrefs

Cf. A000720, A121053, A377994 (complement).

Sequence in context: A340762 A092022 A346302 * A190200 A162902 A026491

Adjacent sequences: A377894 A377895 A377896 * A377898 A377899 A377900

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2024

Status

approved