A350863 Primes p such that p and p+6 are consecutive primes, and p+36 and p+42 are consecutive primes.

47, 131, 331, 557, 571, 941, 977, 1181, 1187, 1621, 1741, 2677, 3691, 3761, 4561, 4951, 5407, 5521, 5807, 5861, 6037, 6317, 6337, 6977, 7481, 7541, 7681, 8081, 8887, 10847, 11897, 12511, 12541, 12547, 12577, 13591, 14717, 15227, 15271, 15761, 15767, 19231, 19441, 22031, 22901, 23167, 25111, 25147

Offset

1,1

Comments

Intersection of A031924 and its translate by -36.

Links

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

Example

a(3) = 331 is a term because 331 and 331+6 = 337 are consecutive primes and 331+36 = 367 and 331+42 = 373 are consecutive primes.

Maple

P:= {seq(ithprime(i), i=1..3000)}:
R:= P intersect map(`-`, P, 6) intersect map(`-`, P, 36) intersect map(`-`, P, 42) minus map(`-`, P, 2) minus map(`-`, P, 4) minus map(`-`, P, 38) minus map(`-`, P, 40):
sort(convert(R, list));

Mathematica

Select[Range[25000], And @@ PrimeQ[(ps = # + {0, 36})] && NextPrime[ps] == ps + {6, 6} &] (* Amiram Eldar, Jan 20 2022 *)
Select[Select[Partition[Prime[Range[3000]], 2, 1], #[[2]]-#[[1]]==6&][[;; , 1]], PrimeQ[#+36]&& NextPrime[ #+36] ==#+42&] (* Harvey P. Dale, Mar 04 2024 *)

Crossrefs

Cf. A031924.

Sequence in context: A235176 A044298 A044679 * A253225 A039530 A288408

Adjacent sequences: A350860 A350861 A350862 * A350864 A350865 A350866

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 19 2022

Status

approved