

A302692


Primes p that are the sum of another prime q and the greatest k such that k! < p.


1



5, 41, 47, 71, 83, 101, 107, 113, 733, 739, 757, 827, 829, 859, 863, 883, 887, 947, 953, 977, 983, 997, 1019, 1039, 1069, 1093, 1097, 1103, 1109, 1123, 1129, 1187, 1193, 1223, 1229, 1237, 1283, 1289, 1297, 1303, 1307, 1327, 1367, 1373, 1429, 1433, 1439, 1453, 1459
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OFFSET

1,1


COMMENTS

Primes p such that p  A084558(p) is also a prime.
Inspired by the fact that this sequence has a nonempty intersection with A124598.
Let H be the intersection of this sequence and A124598. With some observed exceptions q = 3, 103, 1013, 1223, 2903, ..., if some p in this sequence is in H then the corresponding q also belongs to H. It is unknown whether H is finite.
Based upon the first terms of this sequence, it looks like those k satisfying the definition given in NAME are the even terms of A084558 repeated in certain weakly increasing sequence.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

a(3) = 41 since 41 is the third prime that satisfies the given definition(s) for this sequence. Note that A084558(41) = 4; if we subtract: 414 = 37, which is also a prime. Also p = 41 and q = 37 are consecutive terms in A124598.
a(300) = 49459, because q = 49459  A084558(49459) = 49451 is a prime and p = 49459 is the 300th prime satisfying such property. Also p and q are consecutive terms in A124598.


MAPLE

k:= 0: f:= 1: p:= 1: Res:= NULL: count:= 0:
while count < 100 do
p:= nextprime(p);
while p > f do k:= k+1; f:= f*(k+1) od;
if isprime(pk) then Res:= Res, p; count:= count+1 fi;
od:
Res; # Robert Israel, Jun 10 2018


MATHEMATICA

Select[Prime@ Range[2^8], PrimeQ[#  Block[{k = 1}, While[k! <= #, k++]; k  1]] &] (* Michael De Vlieger, Apr 10 2018 *)


PROG

(PARI) A084558(n)={my(m=0); while(n\=m++, ); m1}
firstTerms(U)={my(L:list=List()); forprime(p=2, nextprime(U), if(ispseudoprime(pA084558(p)), listput(L, p))); return(Vec(L))}


CROSSREFS

Cf. A084558, A124598.
Sequence in context: A326265 A043083 A041599 * A232881 A174054 A106963
Adjacent sequences: A302689 A302690 A302691 * A302693 A302694 A302695


KEYWORD

nonn,look


AUTHOR

R. J. Cano, Apr 08 2018


STATUS

approved



