A338425 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.

3, 4, 25, 27, 41, 54, 103, 124, 140, 147, 149, 151, 186, 247, 271, 306, 345, 347, 354, 377, 398, 430, 464, 473, 504, 577, 578, 670, 682, 709, 767, 771, 787, 821, 823, 825, 827, 870, 1037, 1086, 1124, 1157, 1165, 1167, 1276, 1319, 1388, 1401, 1557, 1600, 1602, 1607, 1722, 1724, 1740, 1828, 1830

Offset: 1

Author

Robert Israel, Oct 25 2020

Keywords

• nonn

Comments

Numbers k such that A031131(k)*A031131(k+3)=A031131(k+1)*A031131(k+2).

Examples

			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.
		

Links

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

Crossrefs

Cf. A031131.

Programs

Maple

P:= [seq(ithprime(i), i=1..2005)]:
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]);