OFFSET
1,1
COMMENTS
Primes p(k) such that the number of distinct prime divisors of all composite numbers between p(k) and p(k+1) is 2. - Amarnath Murthy, Sep 26 2002
LINKS
Ray Chandler, Table of n, a(n) for n = 1..61 (terms < 10^1000, first 49 terms from T. D. Noe)
FORMULA
Primes p such that p+1 = (2^u)*(3^w).
EXAMPLE
a(11)+1 = 2*2*2*3*3*3*3*3*3*3*3*3*3 = 472392.
MATHEMATICA
nn=10^15; Sort[Reap[Do[n=2^i 3^j; If[n<=nn && PrimeQ[n-1] && PrimeQ[n+1], Sow[n-1]], {i, Log[2, nn]}, {j, Log[3, nn]}]][[2, 1]]]
Select[Select[Partition[Prime[Range[38*10^5]], 2, 1], #[[2]]-#[[1]]==2&][[All, 1]], FactorInteger[#+1][[All, 1]]=={2, 3}&] (* The program generates the first 15 terms of the sequence. *)
seq[max_] := Select[Sort[Flatten[Table[2^i*3^j - 1, {i, 1, Floor[Log2[max]]}, {j, 1, Floor[Log[3, max/2^i]]}]]], And @@ PrimeQ[# + {0, 2}] &]; seq[2*10^15] (* Amiram Eldar, Aug 27 2024 *)
CROSSREFS
Apart from initial terms, same as A078883.
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 02 2001
STATUS
approved