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A326583 Integers k >= 0 such that 2*k + 1 is prime or square.

%I A326583 #16 Dec 12 2024 00:55:26
%S A326583 0,1,2,3,4,5,6,8,9,11,12,14,15,18,20,21,23,24,26,29,30,33,35,36,39,40,
%T A326583 41,44,48,50,51,53,54,56,60,63,65,68,69,74,75,78,81,83,84,86,89,90,95,
%U A326583 96,98,99,105,111,112,113,114,116,119,120
%N A326583 Integers k >= 0 such that 2*k + 1 is prime or square.
%H A326583 Robert Israel, <a href="/A326583/b326583.txt">Table of n, a(n) for n = 1..10000</a>
%F A326583 a(n) ~ (n log n)/2. - _Charles R Greathouse IV_, Dec 12 2024
%p A326583 s := n -> if irem(n,2) = 1 and (isprime(n) or issqr(n)) then (n-1)/2 else NULL fi:
%p A326583 seq(s(n), n=0..241);
%t A326583 Select[Range[0, 120], Or[IntegerQ@ Sqrt@ #, PrimeQ@ #] &[2 # + 1] &] (* _Michael De Vlieger_, Jul 15 2019 *)
%o A326583 (PARI) list(lim)=my(v=List()); lim\=1; forprime(p=3,2*lim+1, listput(v,p\2)); forstep(n=1,sqrtint(2*lim+1),2, listput(v,n^2\2)); Set(v) \\ _Charles R Greathouse IV_, Dec 12 2024
%Y A326583 Union of A005097 and A046092.
%Y A326583 Cf. A326581, A065091, A000040, A016754, A000290.
%K A326583 nonn,easy
%O A326583 1,3
%A A326583 _Peter Luschny_, Jul 15 2019