A394373 a(n) is the least integer that is a vampire number in base n (see A014575 for base 10).

575, 320, 108, 192, 312, 432, 680, 1008, 1260, 1972, 2100, 2772, 3100, 4140, 4752, 7280, 6368, 24592, 9020, 10752, 11880, 13140, 15288, 18304, 19229, 21456, 23940, 26460, 29280, 196272, 35360, 37680, 41454, 49280, 49932, 271188, 58520, 64428, 68040, 77700, 78540, 82708, 90068, 97920

Offset

2,1

Links

Michael S. Branicky, Table of n, a(n) for n = 2..348

Prog

(PARI) isv(n, b)=my(v=digits(n, b)); if(#v%2, return(0)); fordiv(n, d, if(#digits(d, b)==#v/2 && #digits(n/d, b)==#v/2 && vecsort(v)==vecsort(concat(digits(d, b), digits(n/d, b))) && (d%b || (n/d)%b), return(1))); 0;
a(n) = my(k=1); while (!isv(k, n), k++); k;
(Python)
from itertools import count
from sympy import divisors
from sympy.ntheory.factor_ import digits
def is_vampire(n, base):
    s = sorted(digits(n, base)[1:])
    if len(s)&1: return False
    divs, L, U = divisors(n), base**((len(s)//2)-1), base**(len(s)//2)
    for i in range((len(divs)+1)//2+1):
        x, y = divs[i], divs[-1-i]
        if L <= x < U and L <= y < U and (x%base or y%base):
            t, u = digits(x, base)[1:], digits(y, base)[1:]
            if len(t) == len(u) and sorted(t+u) == s:
                return True
    return False
def a(n):
    for d in count(2, 2):
        v = next((k for k in range(n**(d-1), n**d) if is_vampire(k, n)), None)
        if v: return v
print([a(n) for n in range(2, 46)]) # Michael S. Branicky, Jun 12 2026

Crossrefs

Cf. A014575 (base 10), A392325 (base 12).

Sequence in context: A321052 A369625 A291133 * A027456 A158372 A230353

Adjacent sequences: A394370 A394371 A394372 * A394374 A394375 A394376

Keyword

nonn,base

Author

Michel Marcus, Jun 12 2026

Status

approved