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

1,1

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)

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000290, A277947, A277948, A277959.

Sequence in context: A011814 A238320 A144766 * A263610 A176923 A058412

Adjacent sequences: A277943 A277944 A277945 * A277947 A277948 A277949

Keyword

nonn,base

Author

Colin Barker, Nov 05 2016

Status

approved