A317579 Integers n such that the digit set of n^2 is {0,1,4,9}.

138, 648, 701, 951, 1007, 1070, 1380, 1393, 3153, 3451, 3743, 3747, 4462, 6357, 6480, 7001, 7010, 7071, 9510, 9701, 10007, 10070, 10097, 10243, 10538, 10700, 13800, 13930, 20247, 20347, 22138, 31530, 34510, 37430, 37470, 37538, 38071, 38602, 44620, 63357, 63403, 63570, 64800

Offset

1,1

Comments

n cannot end in the decimal digits 4, 5 or 6; but it most often ends in 0 since if n is present so is 10*n.

n cannot start with the decimal digits 5 or 8. It usually starts with either 3 or 1.

n must lie between 1*10^k & sqrt(2)*10^k, 2*10^k & sqrt(5)*10^k, 3 & sqrt(12)*10^k, sqrt(14)*10^k & sqrt(15)*10^k, sqrt(19)*10^k & sqrt(20)*10^k, sqrt(40)*10^k & sqrt(45)*10^k, sqrt(49)*10^k & sqrt(50)*10^k, sqrt(90)*10^k & sqrt(92)*10^k, sqrt(94)*10^k & sqrt(95)*10^k, sqrt(99)*10^k & sqrt(100)*10^k; for k>0.

Links

Table of n, a(n) for n=1..43.

Example

138 = 19044 which has only the decimal digits 0, 1, 4 & 9. Therefore it is in the sequence.

Mathematica

fQ[n_] := Union[IntegerDigits[n^2]] == {0, 1, 4, 9}; Select[ Range@ 65000, fQ]

Prog

(PARI) isok(n) = Set(digits(n^2)) == [0, 1, 4, 9]; \\ Michel Marcus, Aug 01 2018

Crossrefs

Cf. A285550, A316969.

Sequence in context: A187206 A168531 A260133 * A281592 A213963 A279964

Adjacent sequences: A317576 A317577 A317578 * A317580 A317581 A317582

Keyword

base,nonn

Author

Robert G. Wilson v, Jul 31 2018

Status

approved