|
|
A067604
|
|
Smallest prime p of two consecutive primes, p < q, such that gcd(p+1, q+1) = 2n.
|
|
7
|
|
|
3, 7, 23, 359, 139, 467, 293, 3391, 1259, 17519, 3739, 7079, 12011, 52639, 18869, 66239, 77383, 27143, 51071, 76039, 119447, 76163, 91033, 226943, 206699, 894451, 327347, 492911, 399793, 195599, 313409, 981823, 829883, 1169939, 302329
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Since all consecutive primes, p < q and p greater than 2, are odd, therefore gcd(p+1, q+1) must be even.
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = 3, the 3rd prime being the first entry in A066940;
a(2) = 7, the 4th prime being the first entry in A066941;
a(3) = 23, the 9th prime being of the first entry in A066942;
a(4) = 359, the 72nd prime being the first entry in A066943;
a(5) = 139, the 34th prime being the first entry in A066944.
|
|
MATHEMATICA
|
a = Table[0, {100}]; p = 3; q = 5; Do[q = Prime[n + 1]; d = GCD[p + 1, q + 1]/2; If[d < 101 && a[[d]] == 0, a[[d]] = n]; b = c, {n, 2, 10^7}]; Prime[a]
|
|
PROG
|
(PARI) a(n)=my(k=2*n); forstep(p=k-1, oo, k, if(isprime(p) && (nextprime(p+1)-p)%k==0, return(p))) \\ Charles R Greathouse IV, Aug 17 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|