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A267767
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Numbers whose base-7 representation is a square when read in base 10.
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1
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0, 1, 4, 13, 19, 27, 46, 49, 64, 81, 117, 139, 165, 190, 196, 225, 313, 361, 433, 460, 571, 603, 637, 705, 748, 837, 883, 931, 981, 1048, 1105, 1222, 1323, 1489, 1560, 1684, 1744, 2028, 2185, 2254, 2346, 2401, 2500, 2601, 2763, 2869, 3084, 3136, 3249, 3364, 3547, 3667, 3865, 3969, 4096
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refs;
listen;
history;
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internal format)
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OFFSET
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1,3
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COMMENTS
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Trivially includes powers of 49, since 49^k = 100..00_7 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 49*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 49^k + 2*7^k + 1 = (7^k+1)^2, k > 0, which yields A033934 when written in base 7.
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 1..10000
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MATHEMATICA
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Select[Range[0, 2 10^4], IntegerQ@Sqrt@FromDigits@IntegerDigits[#, 7] &] (* Vincenzo Librandi, Dec 28 2016 *)
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PROG
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(PARI) is(n, b=7, c=10)=issquare(subst(Pol(digits(n, b)), x, c))
(Python)
A267767_list = [int(s, 7) for s in (str(i**2) for i in range(10**6)) if max(s) < '7'] # Chai Wah Wu, Jan 20 2016
(MAGMA) [n: n in [0..10^4] | IsSquare(Seqint(Intseq(n, 7)))]; // Vincenzo Librandi, Dec 28 2016
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CROSSREFS
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Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4.
For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924.
Sequence in context: A268720 A191253 A075327 * A141491 A292363 A119048
Adjacent sequences: A267764 A267765 A267766 * A267768 A267769 A267770
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KEYWORD
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nonn,base
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AUTHOR
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M. F. Hasler, Jan 20 2016
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STATUS
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approved
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