%I #14 Sep 08 2022 08:45:54

%S 1,5,6,7,8,12,13,14,15,16,17,18,21,31,32,33,34,35,36,37,38,39,40,41,

%T 42,43,44,45,46,47,69,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,

%U 89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108

%N Numbers n such that prime(n) modulo n is less than n/2.

%C The sequence consists largely of long runs of consecutive integers. However, there are also a few isolated integers such that the distance to both neighbor terms is greater than 1: 21, 69, 181, 1052, 4137, 4142, 6466, 63424, 100362.

%e 1 is a term because prime(1) mod 1 = 2 mod 1 = 0 < 1/2; 5 is a term because prime(5) mod 5 = 11 mod 5 = 1 < 5/2; 6 is a term because prime(6) mod 6 = 13 mod 6 = 1 < 6/2.

%o (PARI) for(n=1,300,prime(n)%n<n/2&print1(n","))

%o (Magma) [ n: n in [1..120] | NthPrime(n) mod n lt n/2 ];

%Y Cf. companion sequence A178462.

%K nonn

%O 1,2

%A _Zak Seidov_, Dec 23 2010