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

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A084805 A159020 A015830 * A163672 A216580 A114948

Adjacent sequences: A242095 A242096 A242097 * A242099 A242100 A242101

Keyword

nonn,easy

Author

Mark E. Shoulson, Aug 14 2014

Extensions

Added alternative formulation in comment.

Status

approved