A347567 Positive integers which are not twice a positive square and cannot be written as twice a positive square plus an odd prime or twice a positive square plus twice an odd prime.

1, 3, 4, 6, 10, 17, 20, 26, 62, 68, 74, 116, 122, 137, 170, 182, 227, 254, 260, 428, 452, 740, 758, 878, 977, 1052, 1142, 1187, 1412, 1460, 1493, 1542, 1658, 1982, 2510, 2702, 2828, 3098, 3812, 5777, 5972, 5993, 6638, 7352, 15098, 19268, 43358

Offset

1,2

Comments

Probably finite. No more terms < 10^9.

Asked by an anonymous person on Wikipedia, December 31 2021.

No more terms < 10^11. - Martin Ehrenstein, Jan 15 2022

Links

Table of n, a(n) for n=1..47.

Wikipedia:Reference desk/Mathematics, Original question on Wikipedia December 31 2021

Example

5 is NOT a term because 5 is not twice a square and it can be written as 2*1+3, where 1 is a square and 3 is an odd prime.  But 6 is a term because it cannot be written in this way.

Mathematica

Select[Select[Range@2000, !IntegerQ[Sqrt[#/2]]&], (s=#; Length@Select[Flatten[y/.Solve[2x^2+#*y==s&&x>0&&y>0, {x, y}, Integers]&/@{1, 2}], PrimeQ@#&&#>2&])==0&] (* Giorgos Kalogeropoulos, Jan 03 2022 *)

Crossrefs

Cf. A000040, A000290, A347568.

Sequence in context: A355325 A068922 A032408 * A018908 A353138 A052548

Adjacent sequences: A347564 A347565 A347566 * A347568 A347569 A347570

Keyword

nonn,more

Author

Jud McCranie, Jan 02 2022

Status

approved