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%I #12 Apr 23 2021 01:21:37
%S 3,4,25,27,41,54,103,124,140,147,149,151,186,247,271,306,345,347,354,
%T 377,398,430,464,473,504,577,578,670,682,709,767,771,787,821,823,825,
%U 827,870,1037,1086,1124,1157,1165,1167,1276,1319,1388,1401,1557,1600,1602,1607,1722,1724,1740,1828,1830
%N Numbers k such that the points [prime(k), prime(k+1)], [prime(k+2), prime(k+3)] and [prime(k+4), prime(k+5)] are collinear.
%C Numbers k such that A031131(k)*A031131(k+3)=A031131(k+1)*A031131(k+2).
%H Robert Israel, <a href="/A338425/b338425.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3)=25 is in the sequence because the six primes starting with prime(25)=97 are 97, 101, 103, 107, 109, 113, and the points (97,101), (103,107) and (109,113) are collinear, all being on the line y=x+4.
%p P:= [seq(ithprime(i), i=1..2005)]:
%p select(n -> (P[n+2]-P[n])*(P[n+5]-P[n+1]) = (P[n+3] - P[n+1])*(P[n+4]-P[n]), [$1..2000]);
%Y Cf. A031131.
%K nonn
%O 1,1
%A _Robert Israel_, Oct 25 2020
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