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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 (list; graph; refs; listen; history; text; internal format)
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) (Springer-Verlag, 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

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Last modified January 21 15:16 EST 2021. Contains 340352 sequences. (Running on oeis4.)