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

1,1

Comments

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

Links

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

Example

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.

Mathematica

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 *)

Crossrefs

Subsequence of A244283.

Cf. A344570.

Sequence in context: A114948 A191933 A193097 * A077675 A266988 A248642

Adjacent sequences: A343852 A343853 A343854 * A343856 A343857 A343858

Keyword

nonn,base

Author

Andrew Howroyd, May 26 2021

Status

approved