A338173 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.

2, 7, 11, 13, 18, 22, 49, 58, 69, 70, 75, 85, 111, 116, 122, 123, 127, 132, 182, 206, 210, 225, 226, 236, 244, 253, 260, 269, 275, 284, 299, 300, 321, 328, 351, 364, 388, 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

Offset

1,1

Comments

Numbers k such that |A001223(k+1)^2 - A001223(k)*A001223(k+2)| = 4.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

P:= select(isprime, [2, seq(i, i=3..10000, 2)]):
DP:= P[2..-1]-P[1..-2]:
select(t -> abs(DP[t+1]^2-DP[t]*DP[t+2])=4, [$1..nops(DP)-2]);

Crossrefs

Cf. A001223.

Sequence in context: A140563 A154679 A191052 * A138889 A097143 A038897

Adjacent sequences: A338170 A338171 A338172 * A338174 A338175 A338176

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 14 2020

Status

approved