A343855 - OEIS

%I #60 May 29 2021 09:02:43

%S 11,14,19,41,44,49,91,94,99,164,364,649,816,1441,1961,2256,4841,6256,

%T 7841,31369,46241,51849,54761,73969,79216,94096,116641,141616,148841,

%U 219044,292416,361009,368644,466564,961009,973441,2580644,3249001,4651249,6561001

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

%C The requirement that the second digit is not zero is so that both of the two squares have the same number of digits.

%C For k > 2, the number of k-digit terms is given by A344570(k-1).

%C 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

%H Chai Wah Wu, <a href="/A343855/b343855.txt">Table of n, a(n) for n = 1..2348</a>

%e 14 is a term because both 1 and 4 are square numbers.

%e 164 is a term because both 16 = 4^2 and 64 = 8^2 are square numbers.

%e 1441 is a term because both 144 = 12^2 and 441 = 21^2 are square numbers.

%t sQ[n_] := IntegerQ@Sqrt[n];

%t 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]]]]];

%t Select[Range[11, 10^6], selQ] (* _Jean-François Alcover_, May 29 2021 *)

%Y Subsequence of A244283.

%Y Cf. A344570.

%K nonn,base

%O 1,1

%A _Andrew Howroyd_, May 26 2021