A225218 Square numbers containing all the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

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

Offset: 1

Author

Reiner Moewald, May 02 2013

Keywords

• nonn
• base

Comments

The first term having a repeated digit is 10057482369. - Colin Barker, Jan 15 2014

Examples

			1026753849 is in the sequence because 1026753849 = 32043^2 and 1026753849 contains all ten digits 0, ..., 9.
		

Links

• Reiner Moewald, Table of n, a(n) for n = 1..4865

Crossrefs

Supersequence of A036745.

Cf. A235717-A235724.

Programs

Mathematica

Select[#^2 &[Range[1000000]], Length[Union[IntegerDigits[#]]] == 10 &] (* Geoffrey Critzer, Jan 04 2015 *)

PARI

s=[]; for(n=1, 100000, if(#vecsort(eval(Vec(Str(n^2))), , 8)==10, s=concat(s, n^2))); s \\ Colin Barker, Jan 15 2014

Python

from itertools import count, islice
def c(n): return len(set(str(n))) == 10
def agen(): yield from (k*k for k in count(31622) if c(k*k))
print(list(islice(agen(), 21))) # Michael S. Branicky, Dec 27 2022

Formula

a(n) = A054038(n)^2. - Colin Barker, Jan 15 2014