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3, 6, 6, 6, 6, 12, 6, 6, 6, 12, 12, 6, 12, 6, 6, 18, 6, 12, 18, 6, 6, 12, 6, 30, 6, 6, 12, 6, 6, 6, 12, 12, 18, 6, 30, 6, 6, 24, 6, 12, 18, 12, 12, 6, 12, 6, 12, 12, 12, 6, 12, 36, 6, 6, 18, 6, 6, 18, 24, 6, 6, 6, 18, 6, 18, 18, 24, 18, 12, 24, 12, 12, 6, 12, 18, 6, 18, 6, 24
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OFFSET
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1,1
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COMMENTS
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Sequence of differences between consecutive primes of the form 3n-1, which is the sequence A003627.
For n > 1, this is the sequence of first differences of A007528. The longest run of 6's will have length 4 (corresponding to 5, 11, 17, 23, 29 in A007528). Since no other prime ends in 5, thereafter, a run of 6's cannot exceed length 3 (e.g., 41, 47, 53, 59 in A007528). Similarly, a run of 12's cannot exceed length 3 (e.g., 467, 479, 491, 503 in A007528), a run of 18's cannot exceed length 3 (e.g., 2843, 2861, 2879, 2897 in A007528), and a run of 24's cannot exceed length 3 (e.g., 154619, 154643, 154667, 154691 in A007528). This run limit of length 3 also extends to other multiples of 6 that are not divisible by 5. - Timothy L. Tiffin, Dec 22 2022
For multiples of 6 that are divisible by 5, the length of the longest run does not appear to be bounded. For example, if k, k+30, k+60, k+90, ..., k+30(k-1) = 31k-30 are k consecutive primes in A002476, then this will produce a run of k-1 30's in this sequence. - Timothy L. Tiffin, Jan 06 2023
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LINKS
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EXAMPLE
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MATHEMATICA
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Differences[Select[Prime[Range[200]], Mod[#, 3]==2&]] (* Harvey P. Dale, Jan 31 2023 *)
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PROG
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(Python)
from itertools import islice
from sympy import isprime
def A358548_gen(): # generator of terms
p, q = 2, 5
while True:
while not isprime(q):
q += 3
yield q-p
p = q
q += 3
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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