A233998 Values of n such that numbers of the form x^2+n*y^2 for some integers x, y cannot have prime factor of 5 raised to an odd power.

2, 3, 7, 8, 12, 13, 17, 18, 22, 23, 27, 28, 32, 33, 37, 38, 42, 43, 47, 48, 50, 52, 53, 57, 58, 62, 63, 67, 68, 72, 73, 75, 77, 78, 82, 83, 87, 88, 92, 93, 97, 98, 102, 103, 107, 108, 112, 113, 117, 118, 122, 123, 127, 128, 132, 133, 137, 138, 142, 143, 147, 148, 152, 153, 157, 158

Offset

1,1

Comments

Equivalently, this sequence is the union of numbers of the form 25^n*(5*n+2) and numbers of the form 25^n*(5*n+3).

Links

Table of n, a(n) for n=1..66.

Formula

a(n) = 2.4 n + O(log n). - Charles R Greathouse IV, Dec 19 2013

Prog

(PARI) is(n)=n/=25^valuation(n, 25); n%5==2||n%5==3 \\ Charles R Greathouse IV and V. Raman, Dec 19 2013
(Python)
from sympy import integer_log
def A233998(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = 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 n+x-sum(((m:=x//25**i)-2)//5+(m-3)//5+2 for i in range(integer_log(x, 25)[0]+1))
    return bisection(f, n, n) # Chai Wah Wu, Mar 19 2025

Crossrefs

Cf. A055046, A055047, A233999.

Sequence in context: A214324 A102664 A055053 * A047221 A331078 A032967

Adjacent sequences: A233995 A233996 A233997 * A233999 A234000 A234001

Keyword

nonn,easy

Author

V. Raman, Dec 18 2013

Status

approved