A261749 Numbers k where k^2 is an anagram of (k+2)^2.

206, 224, 314, 1799, 2006, 11087, 13364, 15839, 17153, 17324, 20006, 22184, 22706, 24524, 24542, 40031, 40247, 45314, 47069, 48824, 55556, 61694, 64691, 70559, 71351, 89774, 90224, 102374, 108251, 112292, 129824, 132506, 137987, 151757, 154295, 157706, 162089, 167273, 170324, 171557, 175031

Offset: 1

Author

Dhilan Lahoti, Aug 30 2015

Keywords

• nonn
• base
• easy

Comments

Numbers of the form 2*10^k + 6 where k > 1 always appear in this sequence.

Numbers of the form 4*10^k + 31 and 86*10^k + 39 always appear when k > 3.

Similar to A072841 but with (n+2)^2 instead of (n+1)^2.

All numbers in the sequence are of the form 3n + 2.

Multiples of 5 seem to be uncommon.

Another subsequence is numbers of the form 5*(10^(5+9*k)-1)/9 + 1, i.e. 4+9*k 5's followed by a 6: 55556, 55555555555556, 55555555555555555555556, etc. - Robert Israel, Aug 31 2015

Examples

			206 is a term in the sequence because 206^2 (42436) and 208^2 (43264) are anagrams.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072841.

Programs

Maple

filter:= proc(n) local L1, L2;
  L1:= convert(n^2,base,10);
  L2:= convert((n+2)^2,base,10);
  evalb(sort(L1)=sort(L2));
end proc:
select(filter, [3*i+2 $ i = 1..10^5]); # Robert Israel, Aug 31 2015

Mathematica

Select[Range[10^4], Sort[IntegerDigits[#^2]] == Sort[IntegerDigits[(# + 2)^2]] &] (* Typo fixed by Ivan N. Ianakiev, Sep 02 2015 *)

PARI

isok(n) = vecsort(digits(n^2)) == vecsort(digits((n+2)^2)); \\ Michel Marcus, Aug 31 2015

Python

A261749_list = [n for n in range(1,10**6) if sorted(str(n**2)) == sorted(str((n+2)**2))] # Chai Wah Wu, Sep 02 2015