A178462 - OEIS

%I #20 Sep 08 2022 08:45:54

%S 3,4,9,10,11,19,20,22,23,24,25,26,27,28,29,30,48,49,50,51,52,53,54,55,

%T 56,57,58,59,60,61,62,63,64,65,66,67,68,70,71,72,116,122,123,124,125,

%U 126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142

%N Numbers k such that prime(k) mod k > k/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: 116, 4136, 4138, 4141, 4143, 4151, 6458, 63423, 100363.

%e 3 is a term because prime(3) mod 3 = 5 mod 3 = 2 > 3/2;

%e 4 is a term because prime(4) mod 4 = 7 mod 4 = 3 > 4/2;

%e 9 is a term because prime(9) mod 9 = 23 mod 9 = 5 > 9/2.

%t Select[Range[150],Mod[Prime[#],#]>#/2&]  (* _Harvey P. Dale_, Jan 18 2011 *)

%o (PARI) for(n=1,200,prime(n)%n>n/2&print1(n,","))

%o (Magma) [ n: n in [1..150] | NthPrime(n) mod n gt n/2 ];

%Y Cf. companion sequence A178502.

%K nonn

%O 1,1

%A _Zak Seidov_, Dec 24 2010