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

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

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