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
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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);
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Mathematica
Select[Range[0, 120], Or[IntegerQ@ Sqrt@ #, PrimeQ@ #] &[2 # + 1] &] (* Michael De Vlieger, Jul 15 2019 *)
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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