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

Author

Peter Luschny, Jul 15 2019

Keywords

• nonn
• easy

Links

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

Crossrefs

Union of A005097 and A046092.

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

Programs

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 *)

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

Formula

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