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A342150
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Primes p such that three of p+10, p+20, p+30 and p+40 are prime.
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1
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3, 7, 13, 31, 43, 73, 97, 127, 241, 307, 349, 379, 409, 547, 577, 643, 937, 1009, 1021, 1249, 1399, 1597, 1627, 1987, 2341, 2437, 2647, 2689, 2887, 3079, 3517, 3583, 3793, 3823, 4201, 4231, 4243, 4483, 5839, 6091, 6133, 6247, 6679, 6793, 6961, 7477, 7507, 8233, 10303, 12487, 13219, 13411, 13681
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history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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Except for p=3, the three primes must be p+10, p+30 and p+40, because one of p, p+10, p+20 is divisible by 3, and one of p+20, p+30 and p+40 is divisible by 3.
All terms except 3 are == 1 (mod 3).
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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a(3) = 13 is a term because 13, 23, 43 and 53 are all prime.
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MAPLE
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R:= 3: count:= 1:
for p from 7 by 6 while count < 300 do
if andmap(isprime, [p, p+10, p+30, p+40]) then
count:= count+1; R:= R, p
fi
od:
R;
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PROG
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(Python)
from sympy import isprime, primerange
def ok(p): return sum(isprime(p+i*10) for i in range(1, 5)) >= 3
def aupto(lim): return [p for p in primerange(1, lim+1) if ok(p)]
print(aupto(13681)) # Michael S. Branicky, Mar 02 2021
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CROSSREFS
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Sequence in context: A336801 A162869 A079018 * A002383 A163418 A309738
Adjacent sequences: A342145 A342146 A342147 * A342151 A342152 A342153
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot and Robert Israel, Mar 01 2021
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STATUS
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approved
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