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A370139
Primes p such that the sums of three, five, and seven consecutive primes starting with p are prime.
2
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
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
KEYWORD
nonn
AUTHOR
Harvey P. Dale, Feb 11 2024
STATUS
approved