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A192934 Smallest square number starting with (at least) n identical digits. 2
1, 225, 22201, 5555449, 111112681, 3333330225, 555555566736, 2222222266944, 33333333393562596, 88888888888905609, 88888888888905609, 2222222222222640225, 2222222222222640225, 111111111111119590793871025, 5555555555555557064110500049, 11111111111111115805344390916 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: total number of digits of a(n) is always 2*n-1.

This conjecture is false: a(6) = 10 != 2*6-1 = 11.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..150

FORMULA

a(n) = A119998(n)^2.

EXAMPLE

a(2) = 225 because none of 11, 22, 33, 44, 55, 66, 77, 88, 99, any integer from 110 to 119, or any integer from 220 to 224 is a square, but 15^2 = 225.

PROG

(PARI) a(n) = {if (n == 1, return (1)); ok = 0; i = 1; while (! ok, i++; d = digits(i^2, 10); if (#d >= n, ok = 1; for (k = 2, n, if (d[k] != d[1], ok = 0; break; ); ); ); ); return (i^2); } \\ Michel Marcus, Jun 14 2013

CROSSREFS

Cf. A119998, A119511.

Sequence in context: A164752 A151651 A051364 * A264194 A061051 A036428

Adjacent sequences:  A192931 A192932 A192933 * A192935 A192936 A192937

KEYWORD

nonn,base

AUTHOR

J. Lowell, Aug 25 2011

EXTENSIONS

More terms from Alois P. Heinz, Sep 02 2011

STATUS

approved

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Last modified February 22 09:22 EST 2020. Contains 332133 sequences. (Running on oeis4.)