%I #32 Aug 16 2022 16:05:25

%S 2,31,43,67,107,151,167,179,227,233,389,509,547,661,719,769,823,829,

%T 967,1033,1093,1259,1321,1493,1567,1733,1873,2099,2341,2539,2621,2683,

%U 2819,2927,3119,3169,3373

%N Primes p such that the equation prime(p-k)+k! = prime(p) has at least one solution k>0.

%C Apart from the first entry, the majority of the entries stem from k=4, i.e., this is essentially a reverse lookup within A033560. - _R. J. Mathar_, Mar 15 2012

%e 2 is in the sequence because prime(2) = prime(2-1)+1 = 3,

%e 31 is in the sequence because prime(31) = prime(31-4)+1*2*3*4 = 103+24 = 127,

%e 43 is in the sequence because prime(43) = prime(43-4)+1*2*3*4 = 167+24 = 191.

%o (PARI) is_A207973(n)={local(k);k=1;while((k<n)&&(prime(n-k)+k!)<prime(n),k=k+1);if((k<n)&&(prime(n-k)+k!)==prime(n),isprime(n),0)} \\ _Michael B. Porter_, Mar 22 2012

%Y Cf. A000040, A000142.

%K nonn

%O 1,1

%A _Gerasimov Sergey_, Mar 02 2012