A132391 -id:A132391 - cp's OEIS frontend

A119866 Numbers whose square starts with 5 identical digits.

10541, 33334, 47141, 57735, 66667, 105409, 105410, 105411, 105412, 105413, 149071, 149072, 149073, 182574, 182575, 182576, 210818, 210819, 235702, 235703, 258198, 258199, 278886, 278887, 298141, 298142, 316227, 333332, 333333, 333334

Offset: 1

Zak Seidov, Aug 04 2006

			10541^2=111112681, 33334^2=1111155556.

Cf. A119511, A131573, A132391, A133183.

Select[ Range[ 100, 500000 ], Length[ Union[ Take[ IntegerDigits[ #^2 ], 5 ] ] ] == 1 & ] (* Jonathan Vos Post, Aug 29 2007 *)

A346940 Numbers whose square starts with exactly 4 identical digits.

Original entry on oeis.org

2357, 2582, 3334, 4714, 5774, 6667, 8165, 8819, 9428, 10542, 10543, 10544, 10545, 14907, 14908, 14909, 18257, 18258, 18259, 21081, 21082, 21083, 23570, 23571, 25819, 25820, 27888, 27889, 29813, 29814, 31622, 33332, 33333, 33335, 33336, 33337, 33338, 33339, 33340, 33341, 33342

Offset: 1

Bernard Schott, Aug 08 2021

If m is a term, 10*m is another term.

Differs from A132391 where only at least 4 identical digits are required; indeed, 10541 is the first term of A132391 that is not in this sequence (see Example section), the next one is 33346.

			2357 is a term because 2357^2 = 5555449 starts with four 5's.
10541 is not a term because 10541^2 = 111112681 starts with five 1's.

Cf. A346941, A346942.
Supersequences: A131573, A132391.
Similar with: A346812 (2 digits), A346891 (3 digits).

q[n_] := SameQ @@ (d = IntegerDigits[n^2])[[1 ;; 4]] && d[[5]] != d[[1]]; Select[Range[100, 33350], q] (* Amiram Eldar, Aug 08 2021 *)

def ok(n):
    s = str(n*n)
    return len(s) > 4 and s[0] == s[1] == s[2] == s[3] != s[4]
print(list(filter(ok, range(33343)))) # Michael S. Branicky, Aug 08 2021

A167712 a(n) = the smallest positive number, not ending in 0, whose square has a substring of exactly n identical digits.

Original entry on oeis.org

1, 12, 38, 1291, 10541, 57735, 364585, 1197219, 50820359, 169640142, 298142397, 4472135955, 1490711985, 2185812841434

Offset: 1

Zak Seidov, Nov 10 2009

			a(1)=1: 1^2=1 (1 one), a(1)=A119511(1)=A119998(1)
a(2)=12: 12^2=144 (2 fours)
a(3)=38: 38^2=1444 (3 fours)
a(4)=1291: 1291^2=1666681 (4 sixes)
a(5)=10541: 10541^2=111112681 (5 ones), a(5)=A119511(5)=A119998(5)
a(6)=57735: 57735^2=3333330225 (6 threes), a(6)=A119511(6)=A119998(6)
a(7)=364585: 364585^2=132922222225 (7 twos)
a(8)=1197219: 1197219^2=1433333333961 (8 threes)
a(9)=50820359: 50820359^2=2582708888888881 (9 eights)
a(10)=169640142: 169640142^2=28777777777780164 (10 sevens)
a(11)=298142397: 298142397^2=88888888888905609 (11 eights), a(11)=A119511(11)=A119998(11)
a(12)=4472135955: 4472135955^2=20000000000003762025 (12 zeros)
a(13)=1490711985: 1490711985^2=2222222222222640225 (13 twos), a(13)=A119511(13)=A119998(12,13).

Cf. A119511, A119998, A131573, A132391, A119866, A119887, A285056.

a[n_] := Block[{k=1}, While[Mod[k, 10] == 0 || !MemberQ[Length /@ Split[ IntegerDigits[ k^2]], n], k++]; k]; Array[a, 7] (* Giovanni Resta, Apr 11 2017 *)

a(14) from Giovanni Resta, Apr 11 2017

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A119866 Numbers whose square starts with 5 identical digits.

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A346940 Numbers whose square starts with exactly 4 identical digits.

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A167712 a(n) = the smallest positive number, not ending in 0, whose square has a substring of exactly n identical digits.

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