

A242098


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


1



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
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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 nth 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=(_ in count(1) if isprime(_ % floor(sqrt(_))))
[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



