A242098 Numbers n such that the residue of n modulo floor(sqrt(n)) is prime.

11, 14, 18, 19, 22, 23, 27, 28, 32, 33, 38, 39, 41, 44, 45, 47, 51, 52, 54, 58, 59, 61, 66, 67, 69, 71, 74, 75, 77, 79, 83, 84, 86, 88, 92, 93, 95, 97, 102, 103, 105, 107, 112, 113, 115, 117, 123, 124, 126, 128, 134, 135, 137, 139, 146, 147, 149

Offset: 1

Author

Mark E. Shoulson, Aug 14 2014

Keywords

• nonn
• easy

Comments

Also, i^2+p(1), i^2+p(2),..., i^2+p(k), i^2+i+p(1), i^2+i+p(2),..., i^2+i+p(k), for i>=3, where p(n) is the n-th prime and p(k) is the largest prime strictly less than i.

Examples

			floor(sqrt(28)) = 5. 28 modulo 5 = 3, which is prime, so 28 is in the sequence.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Select[Range[200],PrimeQ[ Mod[#,Floor[Sqrt[#]]]]&] (* Harvey P. Dale, May 31 2019 *)

PARI

for(n=1, 10^3, if(isprime(n%sqrtint(n)), print1(n", "))) \\ Jens Kruse Andersen, Aug 16 2014

Python

from sympy import isprime
from math import sqrt, floor
from itertools import count
sequence = ( for  in count(1) if isprime( % floor(sqrt())))
print([next(sequence) for i in range(50)])

Extensions

Added alternative formulation in comment.