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A343855
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Numbers whose second digit is not zero and such that removing either the first or last digit leaves a square number.
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2
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11, 14, 19, 41, 44, 49, 91, 94, 99, 164, 364, 649, 816, 1441, 1961, 2256, 4841, 6256, 7841, 31369, 46241, 51849, 54761, 73969, 79216, 94096, 116641, 141616, 148841, 219044, 292416, 361009, 368644, 466564, 961009, 973441, 2580644, 3249001, 4651249, 6561001
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OFFSET
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1,1
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COMMENTS
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The requirement that the second digit is not zero is so that both of the two squares have the same number of digits.
For k > 2, the number of k-digit terms is given by A344570(k-1).
All terms have last digit either 1, 4, 6, or 9. A term cannot have last digit 0 since that would mean one of the squares ends in an odd number of zeros and all squares end in an even number of zeros. A term cannot have last digit 5 since squares ending in 5 have 25 as last 2 digits and there are no squares having last digit 2. The last 2 digits of terms must be one of 01, 04, 09, 16, 41, 44, 49, 56, 61, 64, 69, 96. - Chai Wah Wu, May 27 2021
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LINKS
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EXAMPLE
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14 is a term because both 1 and 4 are square numbers.
164 is a term because both 16 = 4^2 and 64 = 8^2 are square numbers.
1441 is a term because both 144 = 12^2 and 441 = 21^2 are square numbers.
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MATHEMATICA
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sQ[n_] := IntegerQ@Sqrt[n];
selQ[n_] := With[{dd = IntegerDigits[n]}, If[dd[[2]] == 0 || FreeQ[dd[[-1]], 1|4|6|9], False, sQ[FromDigits[Rest[dd]]] && sQ[FromDigits[Most[dd]]]]];
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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