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

1,1

Comments

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

Links

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

Example

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.

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]);

Crossrefs

Cf. A031131.

Sequence in context: A093600 A128778 A362165 * A304210 A245244 A009391

Adjacent sequences: A338422 A338423 A338424 * A338426 A338427 A338428

Keyword

nonn

Author

Robert Israel, Oct 25 2020

Status

approved