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A308249
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Squares of automorphic numbers in base 12 (cf. A201918).
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0
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0, 1, 16, 81, 4096, 6561, 263169, 1478656, 40960000, 205549569, 54988374016, 233605955584, 6263292059649, 303894740860929, 338531738189824, 170196776412774400, 709858175909625856, 18638643564726714369, 124592287100855910400, 2576097707358918017025, 479214351668445504864256
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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4096 = 2454_12 and sqrt(2454_12) = 54_12. Hence 4096 is in the sequence.
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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