A034978 -id:A034978 - cp's OEIS frontend

A034979 Smallest square starting with a string of n 1's.

1, 1156, 111556, 11115556, 111112681, 111111555556, 11111115555556, 1111111155555556, 111111111555555556, 11111111115555555556, 111111111113333185156, 11111111111122500004921, 11111111111115555555555556, 111111111111119590793871025, 11111111111111115805344390916, 11111111111111115805344390916, 111111111111111115889741773581604, 11111111111111111167337156002376484, 11111111111111111115555555555555555556, 1111111111111111111155555555555555555556

Offset: 1

Patrick De Geest, Nov 15 1998

Robert Israel, Table of n, a(n) for n = 1..498

Cf. A034978, A102807.

f:= proc(n) local x,k,s;
  x:= (10^n-1)/9;
  for k from 0 do
    s:= ceil(sqrt(10^k*x))^2;
    if s < (x+1)*10^k then return s fi
  od
end proc:
map(f, [$1..20]); # Robert Israel, May 31 2023

a(n) <= A102807(n). - Robert Israel, May 31 2023

More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 23 2001

A048346 a(n)^2 is the smallest square containing exactly n 1's in its decimal notation.

Original entry on oeis.org

0, 1, 11, 109, 1054, 3381, 10541, 105414, 414139, 1055041, 10252371, 78173596, 334082481, 1187901979, 1055036071, 33333407869, 105409293239, 718412219489, 1054501356619, 10536182856619, 105409445099152, 333331983425106, 1054092079569499, 10541257568071331, 37564758898655414, 33333331983425106

Offset: 0

Patrick De Geest, Mar 15 1999

Eric Weisstein's World of Mathematics, Square Number

Cf. A036508, A034978.

a[n_] := Block[{k=0}, While[DigitCount[k^2, 10, 1] != n, k++]; k]; Array[a, 8, 0] (* Giovanni Resta, Jul 27 2018 *)

More terms from Jon E. Schoenfield, Jan 11 2009
Initial zero added by Zak Seidov, Nov 22 2010
a(17)-a(19) from Giovanni Resta, Jul 27 2018
a(20)-a(25) from Max Alekseyev, Mar 06 2025

cp's OEIS Frontend

A034979 Smallest square starting with a string of n 1's.

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