A077440 Squares and their roots having square decimal digits.

0, 1, 100, 10000, 1000000, 1100401, 100000000, 110040100, 10000000000, 10100049001, 11004010000, 1000000000000, 1010004900100, 1100401000000, 100000000000000, 100100004990001, 101000490010000, 110040100000000

Offset: 1

Author

Reinhard Zumkeller, Nov 06 2002

Keywords

• nonn
• base

Comments

If k is a term, then so is 100 * k. - Robert Israel, Aug 26 2024

Examples

			a(6) = 1100401 = 1049^2.
A019544(8)=441 is not a term, as 441=21^2 and 2 is not a square digit.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..388

Crossrefs

a(n) = A077439(n)^2.

Cf. A019544, A000290, A046030.

Programs

Maple

N:= 30: # for terms of up to 2*N digits
R:= {1}: T:= {1,9}:
for d from 2 to N do
  T:= select(t -> convert(convert(t^2 mod 10^d, base,10),set) subset {0,1,4,9}, map(t -> (t, t + 10^(d-1), t + 4*10^(d-1), t + 9*10^(d-1)), T));
  R:= R union select(t -> convert(convert(t^2,base,10),set) subset {0,1,4,9},T);
od:
R2:= map(t -> t^2, R):
Res:= map(t -> seq(t*10^(2*i), i=0..(2*N-ilog10(t)-1)/2), R2) union {0}:
sort(convert(Res,list)); # Robert Israel, Aug 26 2024

Mathematica

a = {}; Do[d = FromDigits[ ReplaceAll[ IntegerDigits[n, 4], {3 -> 9, 2 -> 4}]]; If[ Union[ Join[ IntegerDigits[d^2], {0, 1, 4, 9}]] == {0, 1, 4, 9}, a = Append[a, d^2]], {n, 0, 3*10^4}]; a

Extensions

Edited by Robert G. Wilson v, Nov 08 2002