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A243411 Least prime p such that p*10^n-1, p*10^n-3, p*10^n-7 and p*10^n-9 are all prime. 0

%I #11 Jun 12 2016 08:58:52

%S 2,2,10193,24851,20549,719,22133,230471,46679,432449,114689,227603,

%T 305297,61463,1866467,866309,1189403,362081,2615783,493433,966353,

%U 4154363,6562931,9096203,3701627,3128813,20983727,303593,24437537,1068491

%N Least prime p such that p*10^n-1, p*10^n-3, p*10^n-7 and p*10^n-9 are all prime.

%t lpp[n_]:=Module[{p=2,c=10^n},While[!AllTrue[p*c-{1,3,7,9}, PrimeQ], p= NextPrime[ p]];p]; Array[lpp,30] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jun 12 2016 *)

%o (Python)

%o import sympy

%o from sympy import isprime

%o from sympy import prime

%o def a(n):

%o ..for k in range(1,10**8):

%o ....if isprime(prime(k)*10**n-1) and isprime(prime(k)*10**n-3) and isprime(prime(k)*10**n-7) and isprime(prime(k)*10**n-9):

%o ......return prime(k)

%o n = 1

%o while n < 100:

%o ..print(a(n),end=', ')

%o ..n+=1

%o (PARI) a(n)=for(k=1,10^8,if(ispseudoprime(prime(k)*10^n-1) && ispseudoprime(prime(k)*10^n-3) && ispseudoprime(prime(k)*10^n-7) && ispseudoprime(prime(k)*10^n-9), return(prime(k))))

%o n=1;while(n<100,print1(a(n),", ");n++)

%Y Cf. A242564, A064432.

%K nonn

%O 1,1

%A _Derek Orr_, Jun 04 2014

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Last modified July 18 18:59 EDT 2024. Contains 374388 sequences. (Running on oeis4.)