A000404 -id:A000404 - cp's OEIS frontend

A155717 Numbers of the form N = a^2 + 7b^2 for some positive integers a,b.

8, 11, 16, 23, 29, 32, 37, 43, 44, 53, 56, 64, 67, 71, 72, 77, 79, 88, 92, 99, 107, 109, 112, 113, 116, 121, 127, 128, 137, 144, 148, 149, 151, 161, 163, 172, 176, 179, 184, 191, 193, 197, 200, 203, 207, 211, 212, 224, 232, 233, 239, 253, 256, 259, 261, 263, 268

Offset: 1

M. F. Hasler, Jan 25 2009

Subsequence of A020670 (which allows for a and b to be zero).

If N=a^2+7*b^2 is a term then 7*N=(7*b)^2+7*a^2 is also a term. Conversely,if 7*N is a term then N is a term. Example: N=56; N/7=8 is a term, N*7=7^2+7*7^2 is a term. Sequences A154777, A092572 and A154778 have the same property with 7 replaced by prime numbers 2,3 and 5 respectively. - Jerzy R Borysowicz, May 22 2020

Cf. A000404, A154777, A092572, A097268, A154778, A155707-A155716, A155560-A155578.

Select[Range[300], Reduce[a>0 && b>0 && # == a^2 + 7b^2, {a, b}, Integers] =!= False&] (* Jean-François Alcover, Nov 17 2016 *)

isA155717(n,/* optional 2nd arg allows us to get other sequences */c=7) = { for(b=1,sqrtint((n-1)\c), issquare(n-c*b^2) & return(1))}
for( n=1,300, isA155717(n) & print1(n","))

def aupto(limit):
    cands = range(1, int(limit**.5)+2)
    nums = [a**2 + 7*b**2 for a in cands for b in cands]
    return sorted(set(k for k in nums if k <= limit))
print(aupto(268)) # Michael S. Branicky, Aug 11 2021

A070216 Triangle T(n, k) = n^2 + k^2, 1 <= k <= n, read by rows.

Original entry on oeis.org

2, 5, 8, 10, 13, 18, 17, 20, 25, 32, 26, 29, 34, 41, 50, 37, 40, 45, 52, 61, 72, 50, 53, 58, 65, 74, 85, 98, 65, 68, 73, 80, 89, 100, 113, 128, 82, 85, 90, 97, 106, 117, 130, 145, 162, 101, 104, 109, 116, 125, 136, 149, 164, 181, 200, 122, 125, 130, 137, 146, 157

Offset: 1

Charles Northup (cnorthup(AT)esc6.net), May 07 2002

The formula yields squares of hypotenuses of right triangles having integer side lengths (A000404), but with duplicates (cf. A024508) and not in increasing order. - M. F. Hasler, Apr 05 2016

			a(3,2)=13 because 3^2+2^2=13.
Triangle begins:
2;
5, 8;
10, 13, 18;
17, 20, 25, 32;
26, 29, 34, 41, 50;
37, 40, 45, 52, 61, 72;
50, 53, 58, 65, 74, 85, 98;
65, 68, 73, 80, 89, 100, 113, 128;
82, 85, 90, 97, 106, 117, 130, 145, 162;
101, 104, 109, 116, 125, 136, 149, 164, 181, 200; ...
- _Vincenzo Librandi_, Apr 30 2014

Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Not a permutation of sequence A000404 (which has no duplicates).

Cf. A002522 (left edge), A001105 (right edge), A219054 (row sums).

a070216 n k = a070216_tabl !! (n-1) !! (k-1)
a070216_row n = a070216_tabl !! (n-1)
a070216_tabl = zipWith (zipWith (\u v -> (u + v) `div` 2))
                       a215630_tabl a215631_tabl
-- Reinhard Zumkeller, Nov 11 2012

[n^2+k^2: k in [1..n], n in [1..15]]; // Vincenzo Librandi, Apr 30 2014

t[n_,k_]:=n^2 + k^2; Table[t[n, k], {n, 11}, {k, n}]//Flatten (* Vincenzo Librandi, Apr 30 2014 *)

T(n, k) = n^2+k^2;
for (n=1, 10, for(k=1, n, print1(T(n, k), ", "))) \\ Altug Alkan, Mar 24 2016

from math import isqrt
def A070216(n):
    a = (m:=isqrt(k:=n<<1))+(k>m*(m+1))
    return (a*(a*(a*(a-2)-(m:=n<<2)+5)+m)>>2)+n**2 # Chai Wah Wu, Jun 20 2025

a(n, k) = n^2 + k^2, 1 <= k <= n.
T(n,k) = (A215630(n,k) + A215631(n,k)) / 2, 1 <= k <=n. - Reinhard Zumkeller, Nov 11 2012
T(n,k) = A002024(n,k)^2 + A002260(n,k)^2. - David Rabahy, Mar 24 2016

More terms from Larry Reeves (larryr(AT)acm.org), Sep 25 2002

Edited and corrected by M. F. Hasler, Apr 05 2016

A234300 Number of unit squares, aligned with a Cartesian grid, partially encircled along the edge of the first quadrant of a circle centered at the origin ordered by increasing radius.

Original entry on oeis.org

0, 1, 1, 3, 2, 3, 3, 5, 3, 5, 4, 5, 5, 7, 5, 7, 5, 7, 7, 9, 7, 9, 8, 9, 7, 9, 7, 11, 9, 11, 9, 11, 10, 11, 9, 11, 11, 13, 11, 13, 11, 13, 11, 13, 11, 13, 13, 15, 12, 15, 13, 15, 13, 15, 13, 15, 13, 15, 15, 17, 13, 17, 15, 17, 16, 17, 15, 17, 15, 17, 15, 17, 17, 19, 17, 19, 15, 19, 17, 19, 17, 19, 17, 19, 18, 19, 17, 21, 19, 21, 19, 21, 19, 21, 19, 21, 19, 21, 19, 21

Offset: 0

Rajan Murthy, Dec 22 2013

nonn

The first decrease from a(4) = 3 to a(5) = 2 occurs when the radius squared increases from an arbitrary position between 1 and 2 (when 3 squares are on the edge) to exactly 2 (when only 2 squares are on the edge because the circle of square radius 2 passes through the upper right corner on the y=x line). Similar decreases occur when the circle passes through other upper right corners. At least some (if not all) adjacent duplicates occur when the square radius corresponds to a perfect square, that is a corner which is only a lower right corner, i.e., on the y = 0 line. For example, a(6)=a(7)=3 occurs when, for n = 6 , a(n) corresponding to the interval between 2 and 4; and, for n=7, a(n) corresponding to the exact square radius of 4. Some of the confusion may come from the fact that for odd n, there is a unique circle corresponding to elements of a(n) (passing through the corner of specific square(s) on the grid), while for even n, there is a set of circles with a range of radii (which do not pass through corners) corresponding to the elements of a(n). It seems easier to organize the concept in terms of intervals and corners for the sake of consistency.

a(n) is even when the radius squared corresponds to an element of A024517.

			At radius 0, there are no partially filled squares.  At radius >1 but < sqrt(2), there are 3 partially filled squares along the edge of the circle.  At radius = sqrt(2), there are 2 partially filled squares along the edge of the circle.

Rajan Murthy, Table of n, a(n) for n = 0..4999

Cf. A001481 (corresponds to the square radius of alternate entries), A232499 (number of completely encircled squares when the radii are indexed by A000404), A235141 (first differences), A024517.

A237708 is the analog for the 3-dimensional Cartesian lattice and A239353 for the 4-dimensional Cartesian lattice.

function index = n_edgeindex (N)
    if N < 1 then
        N = 1
    end
    N = floor(N)
    i = 0:ceil(N/2)
    i = i^2
    index = i
    for j = 1:length(i)
       index = [index i+ i(j).*ones(i)]
    end
    index = unique(index)
    index = index(1:ceil(N))
    d = diff(index)/2
    d = d +  index(1:length(d))
    index = gsort([index d],"g","i")
    index = index(1:N)
endfunction
function l = n_edge_n (i)
        l=0
        h=0
        while (i > (2*h^2))
            h=h+1
        end
        if i < (2*h^2) then
                l = l+1
        end
        if i >1 then
            t=[0 1]
           while (i>max(t))
               t = [t (sqrt(max(t))+1)^2]
           end
        for j = 1:h
           b=t
           t=[2*(j)^2 (j+1)^2 + (j)^2]
           while (i>max(t))
               t = [t (sqrt(max(t)-(j)^2)+1)^2 + (j)^2]
           end
           l = l+ 2*(length(b)-length(t))
           if max(t) == i then
               l = l-2
           end
        end
       end
endfunction
function a =n_edge (N)
    if N <1 then
        N =1
    end
    N = floor(N)
    a= []
    index = n_edgeindex(N)
    for i = index
        a = [a n_edge_n(i)]
    end
endfunction

a(2k+1) = a(2k) + 2*A000161(A001481(k+1)) - A010052(A001481(k+1)/2). - Rajan Murthy, Jan 14 2013

a(2k) = a(2k-1) - 2*(A000161(A001481(k+1)) - A010052(A001481(k+1))) + A010052(A001481(k+1)/2). - Rajan Murthy, Jan 14 2013

A303375 Numbers of the form a^5 + b^6, with integers a, b > 0.

Original entry on oeis.org

2, 33, 65, 96, 244, 307, 730, 761, 972, 1025, 1088, 1753, 3126, 3189, 3854, 4097, 4128, 4339, 5120, 7221, 7777, 7840, 8505, 11872, 15626, 15657, 15868, 16649, 16808, 16871, 17536, 18750, 20903, 23401, 32432, 32769, 32832, 33497, 36864, 46657, 46688, 46899, 47680, 48393

Offset: 1

M. F. Hasler, Apr 22 2018

Although it is easy to produce many terms of this sequence, it is nontrivial to check whether a very large number is of this form.

This sequence is among others motivated by the hard-to-compute sequence A300567 = numbers z such that z^7 = x^5 + y^6 for some x, y >= 1.

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

Cf. A000404 (a^2 + b^2), A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4).
Cf. A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6).
See also A300567: numbers z such that z^7 = x^5 + y^6 for some x, y >= 1.

is(n,k=5,m=6)=for(b=1,sqrtnint(n-1,m),ispower(n-b^m,n)&&return(b)) \\ Returns b > 0 if n is in the sequence, else 0.
A303375_vec(L=10^5,k=5,m=6,S=List())={for(a=1,sqrtnint(L-1,m),for(b=1,sqrtnint(L-a^m,k), listput(S,a^m+b^k)));Set(S)} \\ all terms up to limit L

a(n) >> n^(30/11). Probably this is the correct asymptotic order. - Charles R Greathouse IV, Jan 23 2025

A336725 A(n,k) is the n-th number that is a sum of k positive k-th powers; square array A(n,k), n>=1, k>=1, read by antidiagonals.

Original entry on oeis.org

1, 2, 2, 3, 5, 3, 4, 10, 8, 4, 5, 19, 17, 10, 5, 6, 36, 34, 24, 13, 6, 7, 69, 67, 49, 29, 17, 7, 8, 134, 132, 98, 64, 36, 18, 8, 9, 263, 261, 195, 129, 84, 43, 20, 9, 10, 520, 518, 388, 258, 160, 99, 55, 25, 10, 11, 1033, 1031, 773, 515, 321, 247, 114, 62, 26, 11, 12, 2058, 2056, 1542, 1028, 642, 384, 278, 129, 66, 29, 12

Offset: 1

Alois P. Heinz, Aug 01 2020

			Square array A(n,k) begins:
   1,  2,  3,   4,   5,   6,    7,    8,    9,   10, ...
   2,  5, 10,  19,  36,  69,  134,  263,  520, 1033, ...
   3,  8, 17,  34,  67, 132,  261,  518, 1031, 2056, ...
   4, 10, 24,  49,  98, 195,  388,  773, 1542, 3079, ...
   5, 13, 29,  64, 129, 258,  515, 1028, 2053, 4102, ...
   6, 17, 36,  84, 160, 321,  642, 1283, 2564, 5125, ...
   7, 18, 43,  99, 247, 384,  769, 1538, 3075, 6148, ...
   8, 20, 55, 114, 278, 734,  896, 1793, 3586, 7171, ...
   9, 25, 62, 129, 309, 797, 2193, 2048, 4097, 8194, ...
  10, 26, 66, 164, 340, 860, 2320, 6568, 4608, 9217, ...

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Columns k=1-11 give: A000027, A000404, A003072, A003338, A003350, A003362, A003374, A003386, A003398, A004810, A004822.
Rows n=1-3 give: A000027, A052944, A145071.
Main diagonal gives A000337.
Cf. A336820.

A:= proc() local l, w, A; l, w, A:= proc() [] end, proc() [] end,
      proc(n, k) option remember; local b; b:=
        proc(x, y) option remember; `if`(x=0, {0}, `if`(y<1, {},
          {b(x, y-1)[], map(t-> t+l(k)[y], b(x-1, y))[]}))
        end;
        while nops(w(k)) < n do forget(b);
          l(k):= [l(k)[], (nops(l(k))+1)^k];
          w(k):= sort([select(h-> h

nmax = 12;
pow[n_, k_] := IntegerPartitions[n, {k}, Range[n^(1/k) // Ceiling]^k];
col[k_] := col[k] = Reap[Module[{j = k, n = 1, p}, While[n <= nmax, p = pow[j, k]; If[p =!= {}, Sow[j]; n++]; j++]]][[2, 1]];
A[n_, k_] := col[k][[n]];
Table[A[n-k+1, k], {n, 1, nmax}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Dec 03 2020 *)

A081324 Twice a square but not the sum of 2 distinct squares.

Original entry on oeis.org

0, 2, 8, 18, 32, 72, 98, 128, 162, 242, 288, 392, 512, 648, 722, 882, 968, 1058, 1152, 1458, 1568, 1922, 2048, 2178, 2592, 2888, 3528, 3698, 3872, 4232, 4418, 4608, 4802, 5832, 6272, 6498, 6962, 7688, 7938, 8192, 8712, 8978, 9522, 10082, 10368, 11552

Offset: 1

Benoit Cloitre, Apr 20 2003

nonn

Conjecture: for n>1 this is A050804.
From Altug Alkan, Apr 12 2016: (Start)
Conjecture is true. Proof :
If n = a^2 + b^2, where a and b are nonzero integers, then n^3 = (a^2 + b^2)^3 = A^2 + B^2 = C^2 + D^2 where;
A = 2*a^2*b + (a^2-b^2)*b = 3*a^2*b - b^3,
B = 2*a*b^2 - (a^2-b^2)*a = 3*a*b^2 - a^3,
C = 2*a*b^2 + (a^2-b^2)*a = 1*a*b^2 + a^3,
D = 2*a^2*b - (a^2-b^2)*b = 1*a^2*b + b^3.
Obviously, A, B, C, D are always nonzero because a and b are nonzero integers. Additionally, if a^2 is not equal to b^2, then (A, B) and (C, D) are distinct pairs, that is, n^3 can be expressible as a sum of two nonzero squares more than one way. Since we know that n is a sum of two nonzero squares if and only if n^3 is a sum of two nonzero squares (see comment section of A000404); if n^3 is the sum of two nonzero squares in exactly one way, n must be a^2 + b^2 with a^2 = b^2 and n is the sum of two nonzero squares in exactly one way. That is the definition of this sequence, so this sequence is exactly A050804 except "0" that is the first term of this sequence. (End) [Edited by Altug Alkan, May 14 2016]
Conjecture: sequence consists of numbers of form 2*k^2 such that sigma(2*k^2)==3 (mod 4) and k is not divisible by 5.
The reason of related observation is that 5 is the least prime of the form 4*m+1. However, counterexamples can be produced. For example 57122 = 2*169^2 and sigma(57122) == 3 (mod 4) and it is not divisible by 5. - Altug Alkan, Jun 10 2016
For n > 0, this sequence lists numbers n such that n is the sum of two nonzero squares while n^2 is not. - Altug Alkan, Apr 11 2016
2*k^2 where k has no prime factor == 1 (mod 4). - Robert Israel, Jun 10 2016

Evan M. Bailey, Table of n, a(n) for n = 1..20000 (first 115 terms from Reinhard Zumkeller, terms 116-1000 from Zak Seidov)
Evan M. Bailey, a081324.cpp

Cf. A050804, A025284, A063725, A125022, A018825, A000404, A004431.

import Data.List (elemIndices)
a081324 n = a081324_list !! (n-1)
a081324_list = 0 : elemIndices 1 a063725_list
-- Reinhard Zumkeller, Aug 17 2011

map(k -> 2*k^2, select(k -> andmap(t -> t[1] mod 4 <> 1, ifactors(k)[2]), [$0..100])); # Robert Israel, Jun 10 2016

Select[ Range[0, 12000], MatchQ[ PowersRepresentations[#, 2, 2], {{n_, n_}}] &] (* Jean-François Alcover, Jun 18 2013 *)

concat([0,2],apply(n->2*n^2, select(n->vecmin(factor(n)[, 1]%4)>1, vector(100,n,n+1)))) \\ Charles R Greathouse IV, Jun 18 2013

A063725(a(n)) = 1. [Reinhard Zumkeller, Aug 17 2011]

a(n) = 2*A004144(n-1)^2 for n > 1. - Charles R Greathouse IV, Jun 18 2013

a(19)-a(45) from Donovan Johnson, Nov 15 2009

Offset corrected by Reinhard Zumkeller, Aug 17 2011

A135789 Positive numbers of the form x^4 - 6 * x^2 * y^2 + y^4 (where x,y are integers).

Original entry on oeis.org

28, 41, 161, 448, 476, 656, 721, 956, 1081, 1241, 1393, 2108, 2268, 2576, 3281, 3321, 3713, 3836, 4633, 4681, 5593, 6076, 7168, 7616, 8188, 9401, 9641, 10496, 11536, 11753, 12121, 12593, 13041, 13916, 15296, 16828, 17296, 17500, 19516, 19856

Offset: 1

Artur Jasinski, Nov 29 2007, Nov 14 2008

nonn

Squares of these numbers are of the form N^4 - M^2 (where N belongs to A135786 and M to A057102). Proof is based on the identity (x^4 - 6x^2 * y^2 + y^4)^2 = (x^2 + y^2)^4 - (4(x^3y - xy^3))^2.
Since x^4 - 6x^2 * y^2 + y^4 = d*d' where d = x^2 - y^2 + 2xy and d' = x^2 - y^2 - 2xy, and d - d' = 4xy, the computational technique is to consider the divisors d|n, d'=n/d, to check that the difference is a multiple of 4, and to check x in the range 1..d/3. - R. J. Mathar, Sep 18 2009
Refers to A057102, which had an incorrect description and has been replaced by A256418. As a result the present sequence should be re-checked. - N. J. A. Sloane, Apr 06 2015

Cf. A000404, A050803, A057102, A135784, A060803, A135786, A135787.

isA135789 := proc(n) for d in numtheory[divisors](n) do dprime := n/d ; if abs(d-dprime) mod 4 = 0 then for x from 1 to d/3 do y := (d-dprime)/4/x ; if type(y,'integer') and y< x and y> 0 then if n = (x^2-y^2+2*x*y)*(x^2-y^2-2*x*y) then RETURN(true); fi; fi; od: fi: od: RETURN(false) ; end: for n from 1 do if isA135789(n) then printf("%d,\n",n) ; fi; od: # R. J. Mathar, Sep 18 2009

a = {}; Do[Do[w = x^4 - 6x^2 y^2 + y^4; If[w > 0&&w<10000, AppendTo[a, w]], {x, y, 2000}], {y, 1, 2000}]; Union[a]

More terms from R. J. Mathar, Sep 18 2009

A140612 Integers k such that both k and k+1 are the sum of 2 squares.

Original entry on oeis.org

0, 1, 4, 8, 9, 16, 17, 25, 36, 40, 49, 52, 64, 72, 73, 80, 81, 89, 97, 100, 116, 121, 136, 144, 145, 148, 169, 180, 193, 196, 225, 232, 233, 241, 244, 256, 260, 288, 289, 292, 305, 313, 324, 337, 360, 361, 369, 388, 400, 404, 409, 424, 441, 449, 457

Offset: 1

Franklin T. Adams-Watters, May 19 2008

Equivalently, nonnegative k such that k*(k+1) is the sum of two squares.
Also, nonnegative k such that k*(k+1)/2 is the sum of two squares. This follows easily from the "sum of two squares theorem": x is the sum of two (nonnegative) squares iff its prime factorization does not contain p^e where p == 3 (mod 4) and e is odd. - Robert Israel, Mar 26 2018
Trivially, sequence includes all positive squares.

			40 = 6^2 + 2^2, 41 = 5^2 + 4^2, so 40 is in the sequence.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A000217, A000290, A000404, A001481, A002378, A050795, A073613.

[k:k in [0..460]| forall{k+a: a in [0,1]|NormEquation(1, k+a) eq true}]; // Marius A. Burtea, Oct 08 2019

(*M6*) A1 = {}; Do[If[SquaresR[2, n (n + 1)/2] > 0, AppendTo[A1, n]], {n, 0, 1500}]; A1
Join[{0}, Flatten[Position[Accumulate[Range[500]], ?(SquaresR[2, #]> 0&)]]] (* _Harvey P. Dale, Jun 07 2015 *)
SequencePosition[Table[If[SquaresR[2,n]>0,1,0],{n,0,500}],{1,1}] [[All,1]]-1 (* Harvey P. Dale, Jul 28 2021 *)

from itertools import count, islice, starmap
from sympy import factorint
def A140612_gen(startvalue=0): # generator of terms >= startvalue
    for k in count(max(startvalue,0)):
        if all(starmap(lambda d, e: e % 2 == 0 or d % 4 != 3, factorint(k*(k+1)).items())):
            yield k
A140612_list = list(islice(A140612_gen(),20)) # Chai Wah Wu, Mar 07 2022

a(1)=0 prepended and edited by Max Alekseyev, Oct 08 2019

A303374 Numbers of the form a^4 + b^6, with integers a, b > 0.

Original entry on oeis.org

2, 17, 65, 80, 82, 145, 257, 320, 626, 689, 730, 745, 810, 985, 1297, 1354, 1360, 2025, 2402, 2465, 3130, 4097, 4112, 4160, 4177, 4352, 4721, 4825, 5392, 6497, 6562, 6625, 7290, 8192, 10001, 10064, 10657, 10729, 14096, 14642, 14705, 15370, 15626, 15641, 15706, 15881

Offset: 1

M. F. Hasler, Apr 22 2018

A subsequence of A000404 (a^2 + b^2), A055394 (a^2 + b^3), A111925 (a^4 + b^2), A100291 (a^4 + b^3), A303372 (a^2 + b^6).

Although it is easy to produce many terms of this sequence, it is nontrivial to check whether a very large number is of this form. Maybe the most efficient way is to consider decompositions of n into sums of two positive squares (see sum2sqr in A133388), and check if one of the terms is a third power and the other a fourth power.

Cf. A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4).

Cf. A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303375 (a^5 + b^6).

Take[Flatten[Table[a^4+b^6,{a,20},{b,20}]]//Union,50] (* Harvey P. Dale, Jul 17 2025 *)

is(n,k=4,m=6)=for(b=1,sqrtnint(n-1,m),ispower(n-b^m,k)&&return(b)) \\ Returns b > 0 if n is in the sequence, else 0.
is(n,L=sum2sqr(n))={for(i=1,#L,L[i][1]&&for(j=1,2,ispower(L[i][j],3)&&issquare(L[i][3-j])&&return(L[i][j])))} \\ See A133388 for sum2sqr(). Much faster than the above for n >> 10^30.
A303374(L=10^5,k=4,m=6,S=[])={for(a=1,sqrtnint(L-1,m),for(b=1,sqrtnint(L-a^m,k),S=setunion(S,[a^m+b^k])));S}

A135790 Positive numbers of the form -x^4+6x^2 y^2-y^4 (where x,y are integers).

Original entry on oeis.org

4, 7, 64, 112, 119, 164, 239, 324, 527, 567, 644, 959, 1024, 1519, 1792, 1904, 2047, 2500, 2624, 2884, 3479, 3824, 4207, 4324, 4375, 4879, 4964, 5184, 5572, 6647, 6887, 7327, 8119, 8432, 9072, 9604, 9639

Offset: 1

Artur Jasinski, Nov 29 2007

nonn

Squares of these numbers are of the form N^4-M^2 (where N belongs to A135786 and M to A057102). Proof uses: (x^4 - 6x^2 y^2 + y^4)^2=(x^2+y^2)^4-(4(x^3y-xy^2))^2.

Refers to A057102, which had an incorrect description and has been replaced by A256418. As a result the present sequence should be re-checked. - N. J. A. Sloane, Apr 06 2015

Cf. A000404, A050803, A057102, A135784, A060803, A135786, A135787, A135789.

a = {}; Do[Do[w = -x^4 + 6x^2 y^2 - y^4; If[w > 0&&w<10000, AppendTo[a, w]], {x, y, 2000}], {y, 1, 2000}]; Union[a]

cp's OEIS Frontend

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