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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. 1
1, 12, 38, 1291, 10541, 57735, 364585, 1197219, 50820359, 169640142, 298142397, 4472135955, 1490711985, 2185812841434 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..14.

EXAMPLE

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).

MATHEMATICA

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 *)

CROSSREFS

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

Sequence in context: A213490 A259517 A303619 * A209872 A186779 A154266

Adjacent sequences:  A167709 A167710 A167711 * A167713 A167714 A167715

KEYWORD

base,nonn,more

AUTHOR

Zak Seidov, Nov 10 2009

EXTENSIONS

a(14) from Giovanni Resta, Apr 11 2017

STATUS

approved

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Last modified March 3 03:03 EST 2021. Contains 341756 sequences. (Running on oeis4.)