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%I #11 Feb 06 2021 22:00:20
%S 2,7,11,13,18,22,49,58,69,70,75,85,111,116,122,123,127,132,182,206,
%T 210,225,226,236,244,253,260,269,275,284,299,300,321,328,351,364,388,
%U 390,391,406,411,413,420,421,422,492,505,518,542,551,558,567,593,611,625,643,658,659,712,713,717,741
%N Numbers k such that the area of the triangle with vertices (prime(k),prime(k+1)), (prime(k+1),prime(k+2)), (prime(k+2),prime(k+3)) is 2.
%C Numbers k such that |A001223(k+1)^2 - A001223(k)*A001223(k+2)| = 4.
%H Robert Israel, <a href="/A338173/b338173.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3)=11 is in the sequence because the 11th through 14th primes are 31, 37, 41, 43, and the area of the triangle with vertices (31,37),(37,41) and (41,43) is |(41-37)^2 - (37-31)*(43-41)|/2 = 2.
%p P:= select(isprime, [2,seq(i,i=3..10000,2)]):
%p DP:= P[2..-1]-P[1..-2]:
%p select(t -> abs(DP[t+1]^2-DP[t]*DP[t+2])=4, [$1..nops(DP)-2]);
%Y Cf. A001223.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Oct 14 2020
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