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A342150 Primes p such that three of p+10, p+20, p+30 and p+40 are prime. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

LINKS

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

EXAMPLE

a(3) = 13 is a term because 13, 23, 43 and 53 are all prime.

MAPLE

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;

PROG

(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

CROSSREFS

Sequence in context: A336801 A162869 A079018 * A002383 A163418 A309738

Adjacent sequences:  A342145 A342146 A342147 * A342151 A342152 A342153

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Mar 01 2021

STATUS

approved

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)