

A338425


Numbers n such that the points [prime(n), prime(n+1)], [prime(n+2), prime(n+3)] and [prime(n+4), prime(n+5)] are collinear.


1



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
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OFFSET

1,1


COMMENTS

Numbers n such that A031131(n)*A031131(n+3)=A031131(n+1)*A031131(n+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: A065809 A093600 A128778 * A304210 A245244 A009391
Adjacent sequences: A338422 A338423 A338424 * A338426 A338427 A338428


KEYWORD

nonn


AUTHOR

Robert Israel, Oct 25 2020


STATUS

approved



