A060211 Larger term of a pair of twin primes such that the 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, 578415690713089, 1141260857376769, 57711166318706689

Offset: 1

Author

Labos Elemer, Mar 20 2001

Keywords

• nonn

Comments

Larger of twin primes p such that p-1 = (2^u)*(3^w), u,w >= 1.

Examples

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

Links

• Ray Chandler, Table of n, a(n) for n = 1..61 (terms < 10^1000)
• Harsh Aggarwal, Table of n, a(n) for n = 62..91 (terms from 10^1000 to 10^20000)

Crossrefs

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

Programs

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 *)

PARI

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

Formula

a(n) = A027856(n+1) + 1. - Amiram Eldar, Mar 17 2025

Extensions

Name corrected by Sean A. Irvine, Oct 31 2022