A072841 -id:A072841 - cp's OEIS frontend

A175518 Numbers n such that 9n+4 are terms in A072841.

1, 17, 101, 501, 1627, 2133, 2143, 2201, 2243, 3086, 3536, 3869, 4163, 4398, 4477, 5598, 5948, 5982, 6101, 6998, 7113, 7807, 8501, 8693, 9177, 9928, 10927, 11127, 11177, 11545, 11836, 12427, 12780, 13043, 13998, 14227, 14448, 14517, 14822

Offset: 1

Zak Seidov, Jun 04 2010

(A072841-4)/9.

A072841

A260477 Numbers n where n^2 is an anagram of (n+1)^2 in base 2.

Original entry on oeis.org

9, 17, 33, 49, 50, 65, 73, 77, 85, 86, 97, 106, 129, 137, 149, 157, 161, 165, 178, 186, 193, 201, 212, 213, 225, 226, 257, 265, 273, 279, 281, 285, 300, 305, 307, 310, 317, 321, 325, 332, 334, 345, 355, 365, 366, 378, 385, 393, 394, 413, 426, 427, 449, 469

Offset: 1

Dhilan Lahoti, Aug 28 2015

Base 2 equivalent of A072841.

It appears that one of these numbers has a 1/n chance of being divisible by an odd number n, but a smaller than 1/n chance if n is even.

			17 is a term of the sequence because its square base 2 (100100001) and 18's square base 2 (101000100) are anagrams.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

For[i = 1, i <= 10000, i++,
If[Sort[IntegerDigits[i^2, 2]] == Sort[IntegerDigits[(i + 1)^2, 2]],
  Print[i]]]

is(n)=hammingweight(n^2)==hammingweight((n+1)^2) && #binary(n^2)==#binary((n+1)^2) \\ Charles R Greathouse IV, Aug 29 2015

a(27)-a(54) from Charles R Greathouse IV, Aug 29 2015

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

Original entry on oeis.org

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

Dhilan Lahoti, Aug 30 2015

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

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

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

Cf. A072841.

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

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

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

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

A130868 Numbers k such that the set of digits of k^2 is the same as the set of digits of (k+1)^2.

Original entry on oeis.org

13, 157, 436, 515, 847, 863, 900, 913, 987, 992, 1010, 1100, 1213, 1350, 1358, 1686, 1784, 2015, 2183, 2263, 2313, 2342, 2597, 2778, 3186, 3279, 3347, 3486, 3536, 3592, 3649, 3779, 3899, 3909, 3913, 3971, 3986, 4012, 4099, 4248, 4284, 4286, 4291, 4412

Offset: 1

Tanya Khovanova, Jul 23 2007

			436^2 = 190096 and 437^2 = 190969 consist of the same digits (although not with the same multiplicities).

The sequence A072841 (digits of k^2 are exactly the same (albeit in different order) as the digits of (k+1)^2) is a subsequence of this sequence.

Select[Range[10000], Union[IntegerDigits[ #^2]] == Union[IntegerDigits[(# + 1)^2]] &]

isok(n) = Set(digits(n^2)) == Set(digits((n+1)^2)); \\ Michel Marcus, Oct 06 2018

A175519 Prime numbers p such that p^2 and (p+1)^2 are anagrams.

Original entry on oeis.org

13, 157, 4513, 19813, 78241, 98347, 111847, 128047, 130657, 161563, 163363, 168457, 205267, 384817, 599341, 602401, 743179, 765031, 833197, 833467, 964021, 996763, 1023133, 1028047, 1200307, 1235263, 1258267, 1478857, 1523551, 1549957

Offset: 1

Zak Seidov, Jun 04 2010

Prime numbers in A072841.

			13^2=169 and 14^2=196,
157^2=24649 and 158^2=24964.

Cf. A072841.

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A175518 Numbers n such that 9n+4 are terms in A072841.

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A260477 Numbers n where n^2 is an anagram of (n+1)^2 in base 2.

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

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A130868 Numbers k such that the set of digits of k^2 is the same as the set of digits of (k+1)^2.

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A175519 Prime numbers p such that p^2 and (p+1)^2 are anagrams.

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