

A018884


Squares using at most two distinct digits, not ending in 0.


3



1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 144, 225, 441, 484, 676, 1444, 7744, 11881, 29929, 44944, 55225, 69696, 9696996, 6661661161
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OFFSET

1,2


COMMENTS

No other terms below 10^41.
The sequence is probably finite.
The two distinct digits of a term cannot both be in the set {0,2,3,7,8}. Looking at the digits (with leading zeros) of i^2 mod 10^4 for 0 <= i < 10^4 shows that there are no repunit terms > 10 and the two distinct digits of a term must be one of the following 21 pairs: '01', '04', '09', '12', '14', '16', '18', '24', '25', '29', '34', '36', '45', '46', '47', '48', '49', '56', '67', '69', '89'.  Chai Wah Wu, Apr 06 2019


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory ΒΆ F24 (at p. 262) (SpringerVerlag, 2d ed. 1994).


LINKS

Table of n, a(n) for n=1..24.
Eric Weisstein's World of Mathematics, Square Number.


MATHEMATICA

Flatten[Table[Select[Flatten[Table[FromDigits/@Tuples[{a, b}, n], {n, 10}]], IntegerQ[ Sqrt[#]]&], {a, 9}, {b, 9}]]//Union (* Harvey P. Dale, Sep 21 2018 *)


CROSSREFS

Cf. A016069, A016070, A018885.
Sequence in context: A068867 A111704 A052041 * A050749 A096599 A016073
Adjacent sequences: A018881 A018882 A018883 * A018885 A018886 A018887


KEYWORD

nonn,base,more,hard


AUTHOR

David W. Wilson


STATUS

approved



