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%I #22 Mar 14 2020 15:52:32
%S 0,1,16,81,4096,6561,263169,1478656,40960000,205549569,54988374016,
%T 233605955584,6263292059649,303894740860929,338531738189824,
%U 170196776412774400,709858175909625856,18638643564726714369,124592287100855910400,2576097707358918017025,479214351668445504864256
%N Squares of automorphic numbers in base 12 (cf. A201918).
%C (sqrt(m))_12 is a suffix of m_12. - _A.H.M. Smeets_, Aug 09 2019
%C 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
%H V. deGuerre and R. A. Fairbairn, <a href="https://oeis.org/A003226/a003226.pdf">Automorphic numbers</a>, J. Rec. Math., 1 (No. 3, 1968), 173-179.
%F Equals A201918(n)^2.
%e 4096 = 2454_12 and sqrt(2454_12) = 54_12. Hence 4096 is in the sequence.
%o (Sage) [(n * n) for n in (0..1000000) if (n * n).str(base = 12).endswith(n.str(base = 12))]
%o (Python)
%o dig = "0123456789AB"
%o def To12(n):
%o s = ""
%o while n > 0:
%o s, n = dig[n%12]+s, n//12
%o return s
%o n, m = 1, 0
%o print(n,m*m)
%o while n < 100:
%o m = m+1
%o m2, m1 = To12(m*m), To12(m)
%o i, i2, i1 = 0, len(m2), len(m1)
%o while i < i1 and (m2[i2-i-1] == m1[i1-i-1]):
%o i = i+1
%o if i == i1:
%o print(n,m*m)
%o n = n+1 # _A.H.M. Smeets_, Aug 09 2019
%Y Cf. A201918, A259468, A259469.
%K nonn,base
%O 1,3
%A _Jeremias M. Gomes_, May 17 2019
%E Terms a(16)..a(21) from _A.H.M. Smeets_, Aug 09 2019
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