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 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. 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 (list; graph; refs; listen; history; text; internal format)
 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: A065809 A093600 A128778 * A304210 A245244 A009391 Adjacent sequences:  A338422 A338423 A338424 * A338426 A338427 A338428 KEYWORD nonn AUTHOR Robert Israel, Oct 25 2020 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)