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A060213
Lesser of twin primes whose average is 6 times a prime.
9
11, 17, 29, 41, 101, 137, 281, 617, 641, 821, 1697, 1877, 2081, 2237, 2381, 2657, 2801, 3461, 3557, 3917, 4637, 4721, 5441, 6197, 6701, 8537, 8597, 9677, 10937, 12161, 12377, 12821, 12917, 13217, 13721, 13757, 13997, 14081, 16061, 17417
OFFSET
1,1
COMMENTS
Lowest factor-density among all positive consecutive integer triples; for p > 41, last digit of p can be only 1 or 7 (see Alexandrov link, p. 15). - Lubomir Alexandrov, Nov 25 2001
LINKS
Lubomir Alexandrov, On the nonasymptotic prime number distribution, arXiv:math/9811096 [math.NT], 1998, see p. 15.
FORMULA
a(n) = 6 * A060212(n) - 1. - Sean A. Irvine, Oct 31 2022
EXAMPLE
102197 is here because 102198 = 17033*6 and 17033 is prime.
MAPLE
map(t -> 6*t-1, select(p -> isprime(p) and isprime(6*p-1) and isprime(6*p+1), [2, seq(i, i=3..10000, 2)]));
MATHEMATICA
Transpose[Select[Partition[Prime[Range[2500]], 2, 1], #[[2]]-#[[1]] == 2 && PrimeQ[Mean[#]/6]&]][[1]] (* Harvey P. Dale, May 04 2014 *)
PROG
(PARI) isok(n) = isprime(n) && isprime(n+2) && !((n+1) % 6) && isprime((n+1)/6); \\ Michel Marcus, Dec 14 2013
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 20 2001
EXTENSIONS
Offset changed to 1 by Michel Marcus, Dec 14 2013
STATUS
approved