A119511
a(n) is the smallest positive integer whose square starts with precisely n identical digits.
Original entry on oeis.org
1, 15, 149, 2357, 10541, 57735, 745356, 1490712, 182574186, 2357022604, 298142397, 7453559925, 1490711985, 10540925533895, 74535599249993, 105409255338946, 7453559924999299, 14907119849998598, 471404520791031683
Offset: 1
Note that 15^2 = 225 and 149^2 = 22201.
A131699
Smallest number whose n-th power begins with precisely n identical digits (in base ten).
Original entry on oeis.org
1, 15, 322, 167, 6444, 32183, 7306, 225418, 6551032, 683405939, 7074698775, 26331754107, 844494314469, 11303028458639, 251188643150958, 93364101391902, 16114920282762613, 239390020079624346, 191165654339590395
Offset: 1
a(1) = 1 because 1^1 = 1 begins with precisely 1 identical digit.
a(2) = 15 because 15^2 = 225 begins with precisely 2 identical digits.
a(3) = 322 because 322^3 = 33386248 begins with precisely 3 identical digits.
a(4) = 167 because 167^4 = 777796321 begins with precisely 4 identical digits.
a(5) = 6444 because 6444^5 = 11111627111310388224 begins with precisely 5 identical digits.
A192934
Smallest square number starting with (at least) n identical digits.
Original entry on oeis.org
1, 225, 22201, 5555449, 111112681, 3333330225, 555555566736, 2222222266944, 33333333393562596, 88888888888905609, 88888888888905609, 2222222222222640225, 2222222222222640225, 111111111111119590793871025, 5555555555555557064110500049, 11111111111111115805344390916
Offset: 1
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.
-
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
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
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).
-
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 *)
A174499
Smallest number whose square starts and ends with (at least) n identical digits.
Original entry on oeis.org
1, 88, 10538, 235700, 10541000, 57735000, 7453560000, 14907120000, 18257418600000, 29814239700000, 298142397000000, 1490711985000000, 14907119850000000, 105409255338950000000, 7453559924999300000000, 10540925533894600000000
Offset: 1
a(3) = 10538 because 10538^2 = 111049444 starts and ends in 3 identical digits.
a(5) = 10541000 because 10541000^2 = 111112681000000 starts with 5 identical digits and ends with 6 identical digits.
-
with(numtheory):T:=array(1..100):p0:=10:for k from 2 to 10 do: id:= 0:for p
from p0 to 100000000 while(id=0) do:n:=p^2:l:=length(n):n0:=n:for m from 1 to
l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :T[m]:=u:od:z:=0:for a from 1
to k-1 do: if T[l]=T[l-a] and T[1]=T[1+a] then z:=z+1:else fi:od:if z=k-1 then
print(p):id:=1:p0:=p:else fi:od:od:
Name clarified and a(10) and a(12) corrected by
Bernard Schott, Aug 08 2021
Showing 1-5 of 5 results.
Comments