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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.
3
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)
Harsh Aggarwal, Table of n, a(n) for n = 62..91 (terms from 10^1000 to 10^20000)
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 20 2001
EXTENSIONS
Name corrected by Sean A. Irvine, Oct 31 2022
STATUS
approved