A377994 Numbers k such that k + PrimePi(k) is odd.

1, 2, 3, 6, 7, 9, 12, 13, 15, 18, 19, 21, 24, 26, 28, 29, 32, 34, 36, 37, 39, 42, 43, 45, 48, 50, 52, 53, 55, 57, 60, 61, 63, 65, 68, 70, 71, 74, 76, 78, 79, 81, 84, 86, 88, 89, 91, 93, 95, 98, 100, 101, 104, 106, 107, 110, 112, 113, 115, 117, 119, 121, 123, 125

Offset: 1

Author

Paolo Xausa, Nov 13 2024

Keywords

• nonn
• easy

Links

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

Crossrefs

Complement of A377897.

Cf. A000720.

Programs

Mathematica

Select[Range[200], OddQ[# + PrimePi[#]] &]

Python

from sympy import prevprime, primepi
def A377994(n):
    def f(x):
        if x<=3: return n
        p = prevprime(x+1)
        i = int(primepi(p))
        return n+(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

Python

from sympy import nextprime
def A377994_gen(): # generator of terms
    p,q,a = 3,5,0
    yield from (1,2)
    while True:
        yield from range(p+a,q,2)
        p, q, a = q, nextprime(q), a^1
A377994_list = list(islice(A377994_gen(),40)) # Chai Wah Wu, Nov 13 2024