A099980 Bisection of A001358.

4, 9, 14, 21, 25, 33, 35, 39, 49, 55, 58, 65, 74, 82, 86, 91, 94, 106, 115, 119, 122, 129, 134, 142, 145, 155, 159, 166, 177, 183, 187, 201, 203, 206, 213, 215, 218, 221, 235, 247, 253, 259, 265, 274, 287, 291, 298, 301, 303, 309, 319, 323, 327, 334, 339, 346

Offset: 0

Author

N. J. A. Sloane, Nov 19 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A001358.

Programs

Maple

P:=[seq(ithprime(n),n=1..100)]: B:={seq(seq(P[i]*P[j],j=1..100),i=1..100)}:C:={seq(B[k],k=1..140)}: seq(C[2*j-1],j=1..70); # Emeric Deutsch, Dec 14 2004

Python

from math import isqrt
from sympy import primepi, primerange
def A099980(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return int((n<<1)+1+x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//p) for p in primerange(s+1)))
    return bisection(f,(n<<1)+1,(n<<1)+1) # Chai Wah Wu, Oct 23 2024

Extensions

More terms from Emeric Deutsch, Dec 14 2004