login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers n such that both n and n squared contain exactly the same digits, and n is not divisible by 10.
1

%I #55 Apr 24 2016 05:55:30

%S 1,4762,4832,10376,10493,11205,12385,14829,23506,24605,26394,34196,

%T 36215,48302,49827,68474,71205,72576,74528,79286,79603,79836,94583,

%U 94867,96123,98376,100469,100496,100498,100499,100946,102245,102953,103265,103479,103756

%N Numbers n such that both n and n squared contain exactly the same digits, and n is not divisible by 10.

%C If n is in this sequence, then n*10^k also satisfies the first portion of the definition for all k >= 0.

%H Chai Wah Wu, <a href="/A258231/b258231.txt">Table of n, a(n) for n = 1..10000</a>

%e 4832 is a term because 4832 squared = 23348224 which contains exactly the same digits as 4832.

%t Select[Select[Range[200000],ContainsExactly[IntegerDigits[ #], IntegerDigits[ #^2]]&], !Divisible[#,10]&]

%o (Python)

%o A258231_list = [n for n in range(10**6) if n % 10 and set(str(n)) == set(str(n**2))] # _Chai Wah Wu_, Apr 23 2016

%Y Cf. A029774, A029793, A257763.

%K nonn,base

%O 1,2

%A _Harvey P. Dale_, Apr 23 2016