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
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..5500
Programs
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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 *)
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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),", ")))
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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)}