A346926 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.

1, 88, 10538, 235700, 0, 57735000, 0, 14907120000, 0, 235702260400000, 0, 7453559925000000, 0, 105409255338950000000, 0, 10540925533894600000000, 0, 14907119849998598000000000, 0, 74535599249992989880000000000, 0, 210818510677891955466600000000000, 0

Offset: 1

Author

Bernard Schott, Aug 07 2021

Keywords

• nonn
• base

Comments

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

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.

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

Examples

			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.
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.
		

Crossrefs

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

Formula

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

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