A346926 - OEIS

%I #13 Aug 08 2021 01:56:57

%S 1,88,10538,235700,0,57735000,0,14907120000,0,235702260400000,0,

%T 7453559925000000,0,105409255338950000000,0,10540925533894600000000,0,

%U 14907119849998598000000000,0,74535599249992989880000000000,0,210818510677891955466600000000000,0

%N a(n) is the smallest positive integer whose square starts and ends with exactly n identical digits, and a(n) = 0 when there is no such integer.

%C When a square ends in exactly three identical digits, these digits are necessarily 444 (A039685).

%C When a square ends with n > 3 identical digits, these last digits are necessarily 0's, and also this is only possible when n is even.

%C Differs from A174499 where only at least n identical digits are required.

%F a(2*n+1) = 0 for n >= 2.

%F a(2*n) = A119511(2*n) * 10^n, for n >= 2.

%e a(2) = 88 because 88^2 = 7744 starts with two 7's and ends with two 4's, and 88 is the smallest integer whose square starts and ends with exactly 2 identical digits.

%e a(4) = 235700 because 235700^2 = 55554490000 starts with four 5's and ends with four 0's, and 235700 is the smallest integer whose square starts and ends with exactly 4 identical digits.

%Y Cf. A039685, A119511, A174499, A346774, A346892.

%K nonn,base

%O 1,2

%A _Bernard Schott_, Aug 07 2021