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

1,1

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)

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 *)

Prog

(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

Crossrefs

Cf. A156977 (square roots).

Sequence in context: A051264 A175845 A225295 * A225218 A359342 A268312

Adjacent sequences: A036742 A036743 A036744 * A036746 A036747 A036748

Keyword

fini,full,nonn,base

Author

David W. Wilson

Status

approved