A360077 Odd numbers k such that k mod (k-s) = 1, where s is the greatest square < k.

3, 7, 11, 13, 19, 21, 27, 29, 31, 33, 41, 43, 51, 53, 55, 57, 61, 67, 71, 73, 83, 85, 89, 91, 97, 103, 109, 111, 123, 125, 127, 129, 131, 133, 141, 155, 157, 171, 173, 175, 177, 181, 183, 193, 199, 201, 209, 211, 227, 229, 233, 239, 241, 253, 259, 261, 271, 273, 291

Offset

1,1

Comments

Sequence contains no terms from A002522. Curiously, the asymptotic density of prime terms appears to be ~ 2n/log(n).

Links

Table of n, a(n) for n=1..59.

Example

Let k =  3; q =  3 - 1^2 = 2 and  3 mod 2  = 1, so  3 is a term.
Let k =  5; q =  5 - 2^2 = 1 and  5 mod 1 != 1, so  5 is not a term.
Let k = 53; q = 53 - 7^2 = 4 and 53 mod 4  = 1, so 53 is a term.

Mathematica

q[n_] := Module[{s = Floor[Sqrt[n - 1]]^2}, Mod[n, n - s] == 1]; Select[Range[1, 300, 2], q] (* Amiram Eldar, Jan 26 2023 *)

Prog

(PARI) is(n)=if(n%2!=0, my(z); sqrtint(n, &z); z>0&&n%z==1);

Crossrefs

Cf. A002496, A002522.

Sequence in context: A045418 A257057 A310197 * A090456 A070303 A256863

Adjacent sequences: A360074 A360075 A360076 * A360078 A360079 A360080

Keyword

nonn

Author

Bill McEachen, Jan 24 2023

Status

approved