|
|
A154553
|
|
Lesser of two consecutive primes, p < q, such that both p*q+p-q and p*q-p+q are prime numbers.
|
|
2
|
|
|
2, 3, 23, 503, 991, 1381, 1621, 3301, 4211, 5471, 5683, 6563, 6581, 7351, 7369, 7829, 8179, 8849, 10061, 11299, 11789, 13841, 14389, 15823, 16981, 17839, 18199, 20563, 21089, 24151, 24989, 25321, 25609, 26203, 28001, 28403, 28433, 32003, 35671
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
2*3-1=5;2*3+1=7, 3*5-2=13;3*5+2=17, ...
|
|
LINKS
|
|
|
MAPLE
|
with(numtheory); A154553:=proc(q) local a, b, n;
for n from 42676 to q do a:=ithprime(n); b:=nextprime(a);
if isprime(a*b+a-b) and isprime(a*b-a+b) then print(a);
|
|
MATHEMATICA
|
lst={}; Do[p=Prime[n]; pn=Prime[n+1]; d=pn-p; If[PrimeQ[p*pn-d]&&PrimeQ[p*pn+d], AppendTo[lst, p]], {n, 8!}]; lst
pnQ[{p_, q_}]:=And@@PrimeQ[{p*q+p-q, p*q-p+q}]; Transpose[Select[ Partition[ Prime[Range[4000]], 2, 1], pnQ]][[1]] (* Harvey P. Dale, Jul 12 2012 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|