A342150 Primes p such that three of p+10, p+20, p+30 and p+40 are prime.

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

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;

Mathematica

Select[Prime[Range[2000]], Total[Boole[PrimeQ[#+{10, 20, 30, 40}]]]==3&] (* Harvey P. Dale, Aug 04 2021 *)

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: A342147 A342148 A342149 * A342151 A342152 A342153

Keyword

nonn

Author

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

Status

approved