login
Primes prime(k) such that ( 9*(prime(k-1) - prime(k-2)) ) | (prime(k)^3 + 1).
0

%I #17 Mar 05 2023 12:10:23

%S 5,11,17,23,47,71,107,113,131,149,179,191,197,233,239,251,269,293,311,

%T 317,353,359,431,467,479,503,521,557,647,683,719,797,809,821,827,839,

%U 857,863,881,887,947,953,971,1019,1031,1061,1097,1103,1151,1163,1223,1259

%N Primes prime(k) such that ( 9*(prime(k-1) - prime(k-2)) ) | (prime(k)^3 + 1).

%e 11 is a term since (11^3 + 1)/(9*(7-5)) = 1332/18 = 74.

%e 131 is a term since (131^3 + 1)/(9*(127-113)) = 2248092/126 = 17842.

%t Select[Partition[Prime[Range[210]], 3, 1], Divisible[(#[[3]]^3 + 1)/9, #[[2]] - #[[1]]] &][[;; , 3]] (* _Amiram Eldar_, Feb 11 2023 *)

%Y Cf. A000040, A030078.

%K nonn

%O 1,1

%A _Najeem Ziauddin_, Feb 11 2023