%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