cp's OEIS Frontend

A267765 Numbers whose base-5 representation is a square when read in base 10.

%I A267765 #16 Jul 02 2019 02:11:26
%S A267765 0,1,4,25,36,49,89,100,121,139,249,329,351,625,676,729,900,961,1225,
%T A267765 1551,1654,2146,2225,2289,2500,2601,3025,3289,3475,3521,3814,4324,
%U A267765 4529,4801,5086,5149,6225,6726,6829,7374,8225,8464,8775,9454,9601,13926,15625,15876,16129,16900,17161
%N A267765 Numbers whose base-5 representation is a square when read in base 10.
%C A267765 Trivially includes powers of 25, since 25^k = 100..00_5 = 10^(2k) when read in base 10. Moreover, for any a(n) in the sequence, 25*a(n) is also in the sequence. One could call "primitive" the terms not of this form, these would be 1, 4, 36 = 121_5, 49 = 144_5, 89 = 324_5, ... These primitive terms include the subsequence 25^k + 2*5^k + 1 = (5^k+1)^2, k > 0, which yields A033934 when written in base 5.
%H A267765 Chai Wah Wu, <a href="/A267765/b267765.txt">Table of n, a(n) for n = 1..10000</a>
%t A267765 Select[Range[0, 17200], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 5] &] (* _Michael De Vlieger_, Jan 24 2016 *)
%o A267765 (PARI) is(n,b=5,c=10)=issquare(subst(Pol(digits(n,b)),x,c))
%o A267765 (Python)
%o A267765 A267765_list = [int(d,5) for d in (str(i**2) for i in range(10**6)) if max(d) < '5'] # _Chai Wah Wu_, Mar 12 2016
%Y A267765 Cf. A267763 - A267769 for bases 3 through 9. The base-2 analog is A000302 = powers of 4.
%Y A267765 For a "prime" analog see also A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924.
%K A267765 nonn,base
%O A267765 1,3
%A A267765 _M. F. Hasler_, Jan 20 2016