A309354 Primes of the form p+q+r where p < q < r = p+6 are consecutive primes.

23, 31, 41, 59, 131, 211, 311, 941, 1049, 1381, 1931, 2579, 3271, 3911, 4289, 4451, 4999, 6421, 6719, 8059, 8069, 9769, 10391, 10399, 10589, 11551, 12011, 14369, 16249, 20479, 23269, 23629, 26591, 27031, 28309, 31379, 33349, 33521, 35339, 35491, 39019, 41081

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Prime Triplet

Example

P = 5 (prime),
P + 2 = 7 (prime),
P + 6 = 11 (prime),
and 5 + 7 + 11 = 23 is prime and is a term.
P = 7 (prime),
P + 4 = 11 (prime),
P + 6 = 13 (prime)
and 7 + 11 + 13 = 31 is prime and is a term.
However, (p,q,r) = (13,17,19) fails because the sum is not a prime.

Mathematica

Select[Total /@ Select[Partition[Prime@Range[2000], 3, 1], #[[3]] == 6 + #[[1]] &], PrimeQ] (* Giovanni Resta, Jul 25 2019 *)

Crossrefs

Cf. A098420.

Sequence in context: A060328 A034962 A133659 * A240725 A106312 A023679

Adjacent sequences: A309351 A309352 A309353 * A309355 A309356 A309357

Keyword

nonn

Author

Philip Mizzi, Jul 25 2019

Extensions

More terms from Giovanni Resta, Jul 25 2019

Status

approved