OFFSET
1,3
COMMENTS
(sqrt(m))_12 is a suffix of m_12. - A.H.M. Smeets, Aug 09 2019
All terms k^2 in this sequence (except the trivials 0 and 1) have a square root k that is the suffix of one of the 12-adic numbers given by A259468 or A259469. From this, the sequence has an infinite number of terms. - A.H.M. Smeets, Aug 09 2019
LINKS
V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179.
FORMULA
Equals A201918(n)^2.
EXAMPLE
4096 = 2454_12 and sqrt(2454_12) = 54_12. Hence 4096 is in the sequence.
PROG
(Sage) [(n * n) for n in (0..1000000) if (n * n).str(base = 12).endswith(n.str(base = 12))]
(Python)
dig = "0123456789AB"
def To12(n):
s = ""
while n > 0:
s, n = dig[n%12]+s, n//12
return s
n, m = 1, 0
print(n, m*m)
while n < 100:
m = m+1
m2, m1 = To12(m*m), To12(m)
i, i2, i1 = 0, len(m2), len(m1)
while i < i1 and (m2[i2-i-1] == m1[i1-i-1]):
i = i+1
if i == i1:
print(n, m*m)
n = n+1 # A.H.M. Smeets, Aug 09 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jeremias M. Gomes, May 17 2019
EXTENSIONS
Terms a(16)..a(21) from A.H.M. Smeets, Aug 09 2019
STATUS
approved