A354284 - OEIS

%I #12 May 31 2022 08:09:03

%S 89,251,449,1061,1439,1741,1997,2237,2239,2267,2593,2657,2699,3301,

%T 3433,3449,5101,5189,5237,5381,6197,6311,6361,6599,6827,6829,6883,

%U 7433,8087,8171,8311,9067,10259,12149,12611,12641,13451,14741,15791,15901,16787,17027,17291,17387,17389,17471,18211

%N The first of four consecutive primes p1, p2, p3, p4 such that (p4-p3)*(p2-p1) = (p3-p2)^2.

%H Robert Israel, <a href="/A354284/b354284.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 449 is a term because the four consecutive primes starting with 449 are 449, 457, 461, 463, and (463-461)*(457-449) = (461-457)^2 = 16.

%p P:= select(isprime, [seq(i,i=3..20000,2)]):

%p R:= select(t -> (P[t+3]-P[t+2])*(P[t+1]-P[t]) = (P[t+2]-P[t+1])^2, [$1..nops(P)-3]):

%p P[R];

%t Select[Partition[Prime[Range[2000]], 4, 1], (#[[4]] - #[[3]])*(#[[2]] - #[[1]]) == (#[[3]] - #[[2]])^2 &][[;; , 1]] (* _Amiram Eldar_, May 23 2022 *)

%o (Python)

%o from sympy import nextprime

%o from itertools import islice

%o def agen(): # generator of terms

%o     p1, p2, p3, p4 = 2, 3, 5, 7

%o     while True:

%o         if (p4-p3)*(p2-p1) == (p3-p2)**2: yield p1

%o         p1, p2, p3, p4 = p2, p3, p4, nextprime(p4)

%o print(list(islice(agen(), 47))) # _Michael S. Branicky_, May 22 2022

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, May 22 2022