A344570 -id:A344570 - cp's OEIS frontend

A343855 Numbers whose second digit is not zero and such that removing either the first or last digit leaves a square number.

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

Offset: 1

Andrew Howroyd, May 26 2021

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

			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.

Chai Wah Wu, Table of n, a(n) for n = 1..2348

Subsequence of A244283.

Cf. A344570.

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]]]]];
Select[Range[11, 10^6], selQ] (* Jean-François Alcover, May 29 2021 *)

cp's OEIS Frontend

A343855 Numbers whose second digit is not zero and such that removing either the first or last digit leaves a square number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica