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A267766
Numbers whose base-6 representation is a square when read in base 10.
2
0, 1, 4, 17, 36, 49, 64, 89, 124, 144, 169, 232, 305, 388, 409, 449, 544, 577, 612, 665, 953, 1105, 1296, 1369, 1444, 1529, 1764, 1849, 1936, 2033, 2304, 2825, 3097, 3204, 3280, 3473, 4345, 4464, 4588, 4841, 5104, 5184, 5329, 5633, 6084, 6241, 7081, 7649, 8044, 8352, 8449, 9160, 9593
OFFSET
1,3
COMMENTS
Trivially includes powers of 36, since 36^k = 100..00_6 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 36*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 36^k + 2*6^k + 1 = (6^k+1)^2, k > 0, which yields A033934 when written in base 6.
MATHEMATICA
Select[Range[0, 10^4], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 6] &] (* Michael De Vlieger, Jan 24 2016 *)
PROG
(PARI) is(n, b=6, c=10)=issquare(subst(Pol(digits(n, b)), x, c))
(Magma) [n: n in [0..10^4] | IsSquare(Seqint(Intseq(n, 6)))]; // Bruno Berselli, Jan 20 2016
(Python)
A267766_list = [int(d, 6) for d in (str(i**2) for i in range(10**6)) if max(d) < '6'] # Chai Wah Wu, Mar 12 2016
CROSSREFS
Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4.
Sequence in context: A009954 A031092 A120884 * A273683 A173511 A218925
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 20 2016
STATUS
approved