

A207973


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


0



2, 31, 43, 67, 107, 151, 167, 179, 227, 233, 389, 509, 547, 661, 719, 769, 823, 829, 967, 1033, 1093, 1259, 1321, 1493, 1567, 1733, 1873, 2099, 2341, 2539, 2621, 2683, 2819, 2927, 3119, 3169, 3373
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..37.


EXAMPLE

2 is in the sequence because prime(2) = prime(21)+1 = 3,
31 is in the sequence because prime(31) = prime(314)+1*2*3*4 = 103+24 = 127,
43 is in the sequence because prime(43) = prime(434)+1*2*3*4 = 167+24 = 191.


PROG

(PARI) is_A207973(n)={local(k); k=1; while((k<n)&&(prime(nk)+k!)<prime(n), k=k+1); if((k<n)&&(prime(nk)+k!)==prime(n), isprime(n), 0)} \\ Michael B. Porter, Mar 22 2012


CROSSREFS

Cf. A000040, A000142.
Sequence in context: A215031 A120638 A101017 * A193423 A241484 A235477
Adjacent sequences: A207970 A207971 A207972 * A207974 A207975 A207976


KEYWORD

nonn


AUTHOR

Gerasimov Sergey, Mar 02 2012


STATUS

approved



