A304441 -id:A304441 - cp's OEIS frontend

A082982 Numbers k such that k, k+1 and k+2 are sums of 2 squares.

0, 8, 16, 72, 80, 144, 232, 288, 360, 520, 576, 584, 800, 808, 1088, 1096, 1152, 1224, 1312, 1600, 1664, 1744, 1800, 1872, 1960, 2248, 2304, 2312, 2384, 2592, 2600, 2824, 3328, 3392, 3528, 3600, 4112, 4176, 4328, 4624, 5120, 5184, 5328, 5408, 5904, 6056

Offset: 1

Xavier Xarles (xarles(AT)mat.uab.es), May 28 2003

All terms are multiples of 8, cf. A304441. - M. F. Hasler, May 13 2018

			80 is here because 80=4^2+8^2, 81=0^2+9^2 and 82=1^2+9^2.

Ivan Neretin, Table of n, a(n) for n = 1..10000
Ajai Choudhry and Bibekananda Maji, Finite sequences of integers expressible as sums of two squares, arXiv:2310.13317 [math.NT], 2023.

Cf. A001481, A050795, A304441.

issumsq(n) = {ok = 0; for (i=0, ceil(sqrt(n/2)), if (issquare(n - i^2), return (1));); return (0);}
isok(n) = issumsq(n) && issumsq(n+1) && issumsq(n+2) \\ Michel Marcus, Jun 30 2013

is_A082982(n)={n%8==0&&is_A001481(n\8)&&is_A001481(n\2+1)&&is_A001481(n+1)} \\ using is_A001481 is much faster than the issumsq() above. - M. F. Hasler, May 13 2018

a(n) = 8*A304441(n). - M. F. Hasler, May 13 2018

More terms from Michel Marcus, Jun 30 2013

A328224 Numbers k such that each of k, k+1, k+2, and k+4 is a sum of two squares.

Original entry on oeis.org

0, 16, 144, 288, 576, 1152, 1600, 2304, 3328, 3600, 4624, 5184, 7056, 8352, 10368, 10656, 10816, 11808, 12112, 12240, 12544, 13120, 13840, 16704, 17424, 19600, 19728, 20736, 20752, 21312, 21904, 22048, 23200, 24480, 24784, 25920, 27792, 28960, 29520, 29824, 30976, 31264, 32400

Offset: 1

Max Alekseyev, Oct 08 2019

nonn

All terms are divisible by 16. - Robert Israel, Oct 10 2019

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001481, A140612, A304441.

Intersection of A082982 and A328223.

[k:k in [0..33000]| forall{k+a: a in [0,1,2,4]|NormEquation(1, k+a) eq true}]; // Marius A. Burtea, Oct 08 2019

ss:=  proc(n) option remember;
  andmap(t -> t[2]::even or t[1] mod 4 <> 3, ifactors(n)[2])
end proc:
select(k -> ss(k) and ss(k+1) and ss(k+2) and ss(k+4), 16*[$0..10^4]); # Robert Israel, Oct 10 2019

ok[n_] := AllTrue[{0,1,2,4}, SquaresR[2, #+n] > 0 &]; Select[ Range[0, 32400], ok] (* Giovanni Resta, Oct 08 2019 *)

A328223 Numbers k such that both k and k+4 are sums of two squares.

Original entry on oeis.org

0, 1, 4, 5, 9, 13, 16, 25, 32, 36, 37, 41, 45, 49, 61, 64, 68, 81, 85, 97, 100, 109, 113, 117, 121, 144, 145, 149, 153, 160, 169, 181, 193, 196, 208, 221, 225, 229, 241, 256, 257, 261, 265, 277, 288, 289, 292, 313, 320, 324, 333, 349, 356, 361, 365, 369, 373, 388, 397, 400

Offset: 1

Max Alekseyev, Oct 08 2019

nonn

Subsequence of A001481. Contains A328224 as a subsequence.

Cf. A140612, A082982, A304441.

[k: k in [0..400] | NormEquation(1, k) eq true and NormEquation(1, k+4) eq true]; // Marius A. Burtea, Oct 08 2019

ok[n_] := AllTrue[{0, 4}, SquaresR[2, # + n] > 0 &]; Select[Range[0, 400], ok] (* Giovanni Resta, Oct 08 2019 *)

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A082982 Numbers k such that k, k+1 and k+2 are sums of 2 squares.

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A328224 Numbers k such that each of k, k+1, k+2, and k+4 is a sum of two squares.

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A328223 Numbers k such that both k and k+4 are sums of two squares.

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