A060211 Larger term of a pair of twin primes such that prime factors of their average are only 2 and 3. Proper subset of A058383.

7, 13, 19, 73, 109, 193, 433, 1153, 2593, 139969, 472393, 786433, 995329, 57395629, 63700993, 169869313, 4076863489, 10871635969, 2348273369089, 56358560858113, 79164837199873, 84537841287169, 150289495621633

Offset

1,1

Links

Ray Chandler, Table of n, a(n) for n = 1..61 (terms < 10^1000)

Formula

Primes such that p + p - 2 = 2p - 2 = (2^u)*(3^w).

Example

a(4)=73, {71,73} are twin primes and (71 + 73)/2 = 72 = 2*2*2*3*3.

Mathematica

Take[Select[Sort[Flatten[Table[2^a 3^b, {a, 250}, {b, 250}]]], AllTrue[#+{1, -1}, PrimeQ]&]+1, 23] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 17 2019 *)

Prog

(PARI) isok(p) = isprime(p) && isprime(p-2) && (vecmax(factor(p-1)[, 1]) == 3); \\ Michel Marcus, Sep 05 2017

Crossrefs

Cf. A001454, A002822, A027856, A033845, A058383, A059960.

Sequence in context: A024732 A024954 A070850 * A355329 A133029 A243962

Adjacent sequences: A060208 A060209 A060210 * A060212 A060213 A060214

Keyword

nonn

Author

Labos Elemer, Mar 20 2001

Extensions

Name corrected by Sean A. Irvine, Oct 31 2022

Status

approved