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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..23.

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

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

Sequence in context: A188991 A189201 A052069 * A174499 A048919 A159718

Adjacent sequences:  A346923 A346924 A346925 * A346927 A346928 A346929

KEYWORD

nonn,base

AUTHOR

Bernard Schott, Aug 07 2021

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)