A036745 Squares including each digit exactly once.

1026753849, 1042385796, 1098524736, 1237069584, 1248703569, 1278563049, 1285437609, 1382054976, 1436789025, 1503267984, 1532487609, 1547320896, 1643897025, 1827049536, 1927385604, 1937408256, 2076351489, 2081549376, 2170348569, 2386517904, 2431870596

Offset: 1

Author

David W. Wilson

Keywords

• fini
• full
• nonn
• base

Comments

The last term of this sequence is a(87) = 9814072356.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..87 (full sequence)

Crossrefs

Cf. A156977 (square roots).

Programs

Maple

lim:=floor(sqrt(9876543210)): for n from floor(sqrt(1023456789)) to lim do d:=[op(convert(n^2, base, 10))]: pandig:=true: for k from 0 to 9 do if(numboccur(k, d)<>1)then pandig:=false: break: fi: od: if(pandig)then printf("%d, ",n^2): fi: od: # Nathaniel Johnston, Jun 22 2011

Mathematica

Select[ Range[ Floor[ Sqrt[ 1023456789 ] ], Floor[ Sqrt[ 9876543210 ] ] ]^2, Union[ DigitCount[ # ] ]== {1} & ]
Select[FromDigits/@Permutations[Range[0,9]],IntegerLength[#]==10&&IntegerQ[ Sqrt[#]]&] (* Harvey P. Dale, Apr 09 2012 *)

Python

def c(n): return len(set(str(n))) == 10
def afull(): return [k*k for k in range(31622, 10**5) if c(k*k)]
print(afull()) # Michael S. Branicky, Dec 27 2022