A243409 Primes p such that 100p-1, 100p-3, 100p-7, and 100p-9 are all prime.

2, 797, 1193, 6803, 15773, 28793, 35507, 41579, 53189, 53279, 57347, 60161, 70457, 77549, 81839, 140549, 143387, 150779, 151241, 164447, 170627, 201011, 255083, 285287, 293831, 300317, 316073, 336671, 343661, 449921, 470087, 486947, 488603, 518801, 556289, 569243, 602087

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..5500

Example

2 is prime, 100*2-1 = 199 is prime, 100*2-3 = 197 is prime, 100*2-7 = 193 is prime, and 100*2-9 = 191 is prime. Thus 2 is a member of this sequence.

Mathematica

Select[Prime[Range[50000]], PrimeQ[100# -1]&&PrimeQ[100# -3]&&PrimeQ[100# -7] &&PrimeQ[100# -9] &] (* K. D. Bajpai, Jun 13 2014 *)
Select[Prime[Range[50000]], AllTrue[100#-{1, 3, 7, 9}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 06 2019 *)

Prog

(Python)
import sympy
from sympy import isprime
from sympy import prime
{print(prime(n), end=', ') for n in range(1, 10**5) if isprime(100*prime(n)-1) and isprime(100*prime(n)-3) and isprime(100*prime(n)-7) and isprime(100*prime(n)-9)}
(PARI) for(n=1, 10^5, if(ispseudoprime(100*prime(n)-1)&& ispseudoprime(100*prime(n)-3)&& ispseudoprime(100*prime(n)-7)&& ispseudoprime(100*prime(n)-9), print1(prime(n), ", ")))

Crossrefs

Cf. A236042, A064976.

Sequence in context: A320481 A078169 A226779 * A281195 A109555 A214898

Adjacent sequences: A243406 A243407 A243408 * A243410 A243411 A243412

Keyword

nonn

Author

Derek Orr, Jun 04 2014

Status

approved