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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 (list; graph; refs; listen; history; text; internal format)
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: A310005 A068922 A032408 * A018908 A353138 A052548

Adjacent sequences:  A347564 A347565 A347566 * A347568 A347569 A347570

KEYWORD

nonn,more

AUTHOR

Jud McCranie, Jan 02 2022

STATUS

approved

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Last modified July 6 11:27 EDT 2022. Contains 355110 sequences. (Running on oeis4.)