A370139 Primes p such that the sums of three, five, and seven consecutive primes starting with p are prime.

19, 29, 31, 53, 79, 379, 401, 839, 883, 1301, 1409, 1951, 1973, 2113, 2683, 2791, 2833, 3407, 3613, 3793, 3823, 4441, 4751, 4831, 5623, 5827, 6133, 6329, 7187, 7237, 7703, 8527, 9173, 10103, 10853, 11317, 12277, 13163, 13933, 14159, 14827, 15241, 15667

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

379 is in the sequence because the seven consecutive primes starting with 379 are 379, 383, 389, 397, 401, 409, and 419, and (379+383+389)=1151, and (379+383+389+397+401)=1949, and (379+383+389+397+401+409+419)=2777, and 1151 and 1949 and 2777 are all primes.

Mathematica

Select[Partition[Prime[Range[5000]], 7, 1], AllTrue[{Total[Take[#, 3]], Total[Take[#, 5]], Total[#]}, PrimeQ]&][[;; , 1]]

Crossrefs

Intersection of A180948 and A182121.

Sequence in context: A067833 A135170 A173959 * A139539 A191047 A047985

Adjacent sequences: A370136 A370137 A370138 * A370140 A370141 A370142

Keyword

nonn

Author

Harvey P. Dale, Feb 11 2024

Status

approved