A071519 Numbers whose square is a zeroless pandigital number (i.e., use the digits 1 through 9 once).

11826, 12363, 12543, 14676, 15681, 15963, 18072, 19023, 19377, 19569, 19629, 20316, 22887, 23019, 23178, 23439, 24237, 24276, 24441, 24807, 25059, 25572, 25941, 26409, 26733, 27129, 27273, 29034, 29106, 30384

Offset: 1

Author

Lekraj Beedassy, Jun 20 2002

Keywords

• fini
• full
• easy
• nonn
• base

Crossrefs

A subset of A054037.

Cf. A036744, A054038, A156977.

Programs

Maple

lim:=floor(sqrt(987654321)): for n from floor(sqrt(123456789)) to lim do d:=[op(convert(n^2, base, 10))]: pandig:=true: for k from 1 to 9 do if(numboccur(k, d)<>1)then pandig:=false: break: fi: od: if(pandig)then printf("%d, ", n): fi: od: # Nathaniel Johnston, Jun 22 2011

Mathematica

Sqrt[#]&/@Select[FromDigits/@Permutations[Range[9]],IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, Sep 23 2011 *)
Select[Range[11112, 31427,3], DigitCount[#^2] == {1,1,1,1,1,1,1,1,1,0} &]  (* Zak Seidov, Jan 11 2012 *)

PARI

A071519 = select( {is_A071519(n,L=[1..9])=vecsort(digits(n^2))==L}, [1e5\9..1e5\3]) \\ M. F. Hasler, Jun 28 2023

Formula

a(n) = sqrt(A036744(n)). - Zak Seidov, Jan 11 2012