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URL: https://oeis.org/A346926

⇱ A346926 - OEIS

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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.
2
1, 88, 10538, 235700, 0, 57735000, 0, 14907120000, 0, 235702260400000, 0, 7453559925000000, 0, 105409255338950000000, 0, 10540925533894600000000, 0, 14907119849998598000000000, 0, 74535599249992989880000000000, 0, 210818510677891955466600000000000, 0
OFFSET
1,2
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.
FORMULA
a(2*n+1) = 0 for n >= 2.
a(2*n) = A119511(2*n) * 10^n, for n >= 2.
EXAMPLE
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
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Aug 07 2021
STATUS
approved