A358705 Zeroless pandigital numbers whose square has each digit 1 to 9 twice.

345918672, 351987624, 359841267, 394675182, 429715863, 439516278, 487256193, 527394816, 527498163, 528714396, 572493816, 592681437, 729564183, 746318529, 749258163, 754932681, 759142683, 759823641, 762491835, 783942561, 784196235, 845691372, 891357624, 914863275, 915786423, 923165487, 928163754, 976825431

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Example

345918672 is a term since its square 119659727638243584 contains all digits 1..9 twice each.

Maple

R:= NULL:
for t in combinat:-permute([$1..9]) do
  x:= add(t[i]*10^(i-1), i=1..9);
  if sort(convert(x^2, base, 10)) = [seq(i$2, i=1..9)] then
    R:= R, x
  fi
od:
sort([R]); # Robert Israel, Nov 27 2022

Prog

(Python)
from itertools import permutations as per
a=[]
for n in [int(''.join(d)) for d in per('123456789', 9)]:
    if all(str(n**2).count(d) ==2 for d in '123456789'):
        a.append(n)
print(a)

Crossrefs

Cf. A050289, A199630.

Sequence in context: A159448 A316745 A351459 * A015381 A257384 A186628

Adjacent sequences: A358702 A358703 A358704 * A358706 A358707 A358708

Keyword

nonn,base,fini,full

Author

Zhining Yang, Nov 27 2022

Status

approved