login
a(n) is the least prime prime(k) for which A351692(k) = n, or 0 if there is no such prime.
2

%I #14 May 11 2022 22:38:20

%S 2,3,29,13,47,19,31,647,101,107,181,569,109,839,199,811,283,373,97,73,

%T 151,79,229,149,103,443,401,701,167,751,1901,347,379,197,157,227,673,

%U 193,383,277,353,991,313,359,419,337,911,461,1319,1279,349,757,2957,1747,827,631,457,1511,1249,1559,1091

%N a(n) is the least prime prime(k) for which A351692(k) = n, or 0 if there is no such prime.

%C a(n) = prime(k) for the least k such that prime(k)+2*prime(k+j) and prime(k)+2*prime(k-j) are both prime for j = n but not both prime for j = 1 ... n-1.

%H Robert Israel, <a href="/A351693/b351693.txt">Table of n, a(n) for n = 0..1000</a>

%e a(3) = 13 = prime(6) because A351692(6) = 3 and A351692(k) <> 3 for 1 <= k < 6.

%p nP:= 10000: Primes:= [seq(ithprime(i),i=1..nP)]: R:= 2: found:= true:

%p for n from 1 to 300 while found do

%p found:= false;

%p for k from n+1 to nP-n do

%p if isprime(Primes[k]+2*Primes[k-n]) and isprime(Primes[k]+2*Primes[k+n]) and

%p andmap(t -> not isprime(Primes[k]+2*Primes[k-t]) or not

%p isprime(Primes[k]+2*Primes[k+t]), [$1..n-1]) then

%p R:= R, Primes[k]; found:= true; break

%p fi

%p od od:

%p R;

%o (PARI) f(n) = for (k=1, n-1, my(p=prime(n)); if (isprime(p + 2*prime(n-k)) && isprime(p + 2*prime(n+k)), return(k))); return(0); \\ A351692

%o a(n) = my(k=1); while (f(k) != n, k++); prime(k); \\ _Michel Marcus_, May 11 2022

%Y Cf. A000040, A351692.

%K nonn

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, May 05 2022