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

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, 41, 44, 48, 50, 51, 53, 54, 56, 60, 63, 65, 68, 69, 74, 75, 78, 81, 83, 84, 86, 89, 90, 95, 96, 98, 99, 105, 111, 112, 113, 114, 116, 119, 120

Offset

1,3

Links

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

Formula

a(n) ~ (n log n)/2. - Charles R Greathouse IV, Dec 12 2024

Maple

s := n -> if irem(n, 2) = 1 and (isprime(n) or issqr(n)) then (n-1)/2 else NULL fi:
seq(s(n), n=0..241);

Mathematica

Select[Range[0, 120], Or[IntegerQ@ Sqrt@ #, PrimeQ@ #] &[2 # + 1] &] (* Michael De Vlieger, Jul 15 2019 *)

Prog

(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

Crossrefs

Union of A005097 and A046092.

Cf. A326581, A065091, A000040, A016754, A000290.

Sequence in context: A164119 A308017 A184107 * A033102 A295796 A030789

Adjacent sequences: A326580 A326581 A326582 * A326584 A326585 A326586

Keyword

nonn,easy

Author

Peter Luschny, Jul 15 2019

Status

approved