OFFSET
1,2
COMMENTS
Note that in contrast to this sequence, which contains 102 terms up to 10^12, the analogous sequence of cubes (A272826) may contain only 3 in total.
Moreover, the similar sequences for the fourth and fifth perfect powers seem to contain only two terms (1, 81) in the case of the former and only one term (1) in the case of the latter. Higher powers also appear to produce sequences with one (mostly) or two terms only.
Unlike the analogous sequence for cubes, this sequence is heuristically infinite. - Charles R Greathouse IV, May 08 2016
This sequence is infinite because it contains the squares of the numbers of the forms 10*(10^k-1)/3+8 and 100*(10^k-1)/3+59. - Giovanni Resta, May 09 2016
Additionally, this sequence contains the squares of the numbers of the form 1000*(10^k-1)/3 + 809 for k > 2. For k > 2, numbers of the form (1000*(10^k-1)/3 + 809)^2 contains all digits that are powers of 2. - Altug Alkan, May 14 2016
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
144 is a term as its digits are only powers of 2 and it is a square, 144 = 12^2.
MATHEMATICA
Select[Range[12000]^2, SubsetQ[{1, 2, 4, 8}, IntegerDigits@#] &]
Select[Flatten[Table[FromDigits/@Tuples[{1, 2, 4, 8}, n], {n, 9}]], IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, Aug 05 2024 *)
PROG
(PARI) is(n)=issquare(n) && #setintersect(Set(digits(n)), [0, 3, 5, 6, 7, 9])==0 \\ Charles R Greathouse IV, May 08 2016
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Waldemar Puszkarz, May 08 2016
STATUS
approved