A059960 Smaller term of a pair of twin primes such that prime factors of their average are only 2 and 3.

5, 11, 17, 71, 107, 191, 431, 1151, 2591, 139967, 472391, 786431, 995327, 57395627, 63700991, 169869311, 4076863487, 10871635967, 2348273369087, 56358560858111, 79164837199871, 84537841287167, 150289495621631, 578415690713087, 1141260857376767

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

Cf. A014574, A002822, A033845, A058383, A027856.

Cf. A052297, A075581, A075580, A075583, A075584, A075585, A075586, A075587, A075588, A075589.

Apart from initial terms, same as A078883.

Sequence in context: A058019 A182482 A075582 * A265850 A185365 A282669

Adjacent sequences: A059957 A059958 A059959 * A059961 A059962 A059963

Keyword

nonn

Author

Labos Elemer, Mar 02 2001

Status

approved