

A267769


Numbers whose base9 representation is a square when read in base 10.


8



0, 1, 4, 15, 23, 33, 58, 73, 81, 100, 121, 185, 213, 265, 298, 324, 361, 400, 474, 509, 555, 643, 685, 751, 861, 914, 1093, 1153, 1215, 1288, 1354, 1481, 1554, 1705, 1783, 1863, 1945, 2029, 2210, 2301, 2488, 2584, 2673, 2773, 2875, 3101, 3210, 3424, 3538, 3682, 3802, 4038, 4154, 4281, 4450
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OFFSET

1,3


COMMENTS

Trivially includes powers of 81, since 81^k = 100..00_9 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 81*a(n) is also in the sequence. One could call "primitive" the terms not of this form. These primitive terms include the subsequence 81^k + 2*9^k + 1 = (9^k+1)^2, k > 0, which yields A033934 when written in base 9.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000


MATHEMATICA

Select[Range[0, 5000], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 9] &] (* Michael De Vlieger, Jan 24 2016 *)


PROG

(PARI) is(n, b=9, c=10)=issquare(subst(Pol(digits(n, b)), x, c))
(Python)
A267769_list = [int(s, 9) for s in (str(i**2) for i in range(10**6)) if max(s) < '9'] # Chai Wah Wu, Jan 20 2016


CROSSREFS

Cf. A267763  A267768 for bases 3 through 8. The base2 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: A055465 A209870 A167293 * A192201 A054308 A051531
Adjacent sequences: A267766 A267767 A267768 * A267770 A267771 A267772


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 20 2016


STATUS

approved



