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URL: https://oeis.org/A347567

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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
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, Dec 31 2021.
No more terms < 10^11. - Martin Ehrenstein, Jan 15 2022
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
KEYWORD
nonn,more
AUTHOR
Jud McCranie, Jan 02 2022
STATUS
approved