A277946 Squares whose largest decimal digit is 2.

121, 10201, 12100, 22201, 1002001, 1020100, 1022121, 1210000, 1212201, 2220100, 100020001, 100200100, 100220121, 102010000, 102212100, 121000000, 121022001, 121220100, 210221001, 222010000, 10000200001, 10002000100, 10002200121, 10020010000, 10020210201

Offset: 1

Author

Colin Barker, Nov 05 2016

Keywords

• nonn
• base

Comments

A subsequence of A000290.

From Robert Israel, Nov 14 2016: (Start)

If n is a term, then so is 100*n.

The first term with an even number of digits is a(36) = 100021020121.

The first term with an even number of digits that is not of the form a(36)*100^k has at least 24 digits.

(End)

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..50 from Colin Barker, terms n = 51..474 from Robert Israel)

Crossrefs

Cf. A000290, A277947, A277948, A277959.

Programs

Magma

[n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 2]; // Vincenzo Librandi, Nov 06 2016

Maple

res:= NULL: B:= [1,2]:
for m from 1 to 10 do
  for q in B do
    for x from ceil(sqrt(10^m*q)) to floor(sqrt(10^m*q + 2/9*(10^m-1))) do
      if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  for q in B do
     for x from ceil(sqrt(10^(m+1)*q)) to floor(sqrt(10^(m+1)*q + 2/9*(10^(m+1)-1))) do
       if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  if m < 10 then B:= map(t -> (10*t,10*t+1,10*t+2),B) fi;
od:
res; # Robert Israel, Nov 14 2016

Mathematica

fQ[n_] := Union[ IntegerDigits[ n^2]][[-1]] == 2; Select[ Range@100500, fQ]^2 (* Robert G. Wilson v, Nov 06 2016 *)

PARI

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==2, listput(L, n^2))); Vec(L)
\\ See A277959 for more efficient code. - M. F. Hasler, Nov 16 2017

Formula

a(n) = A277959(n)^2. Intersection of A000290 and A277964. - M. F. Hasler, Nov 15 2017