cp's OEIS Frontend

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

%I A167712 #10 Apr 14 2017 10:45:14
%S A167712 1,12,38,1291,10541,57735,364585,1197219,50820359,169640142,298142397,
%T A167712 4472135955,1490711985,2185812841434
%N A167712 a(n) = the smallest positive number, not ending in 0, whose square has a substring of exactly n identical digits.
%e A167712 a(1)=1: 1^2=1 (1 one), a(1)=A119511(1)=A119998(1)
%e A167712 a(2)=12: 12^2=144 (2 fours)
%e A167712 a(3)=38: 38^2=1444 (3 fours)
%e A167712 a(4)=1291: 1291^2=1666681 (4 sixes)
%e A167712 a(5)=10541: 10541^2=111112681 (5 ones), a(5)=A119511(5)=A119998(5)
%e A167712 a(6)=57735: 57735^2=3333330225 (6 threes), a(6)=A119511(6)=A119998(6)
%e A167712 a(7)=364585: 364585^2=132922222225 (7 twos)
%e A167712 a(8)=1197219: 1197219^2=1433333333961 (8 threes)
%e A167712 a(9)=50820359: 50820359^2=2582708888888881 (9 eights)
%e A167712 a(10)=169640142: 169640142^2=28777777777780164 (10 sevens)
%e A167712 a(11)=298142397: 298142397^2=88888888888905609 (11 eights), a(11)=A119511(11)=A119998(11)
%e A167712 a(12)=4472135955: 4472135955^2=20000000000003762025 (12 zeros)
%e A167712 a(13)=1490711985: 1490711985^2=2222222222222640225 (13 twos), a(13)=A119511(13)=A119998(12,13).
%t A167712 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 *)
%Y A167712 Cf. A119511, A119998, A131573, A132391, A119866, A119887, A285056.
%K A167712 base,nonn,more
%O A167712 1,2
%A A167712 _Zak Seidov_, Nov 10 2009
%E A167712 a(14) from _Giovanni Resta_, Apr 11 2017