A060213 Lesser of twin primes whose average is 6 times a prime.

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

Author

Labos Elemer, Mar 20 2001

Keywords

• nonn

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

Examples

			102197 is here because 102198 = 17033*6 and 17033 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Lubomir Alexandrov, On the nonasymptotic prime number distribution, arXiv:math/9811096 [math.NT], 1998, see p. 15.

Crossrefs

Cf. A002822, A058383, A059960, A027856, A001454, A001359, A060212.

Programs

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 *)

PARI

isok(n) = isprime(n) && isprime(n+2) && !((n+1) % 6) && isprime((n+1)/6); \\ Michel Marcus, Dec 14 2013

Formula

a(n) = 6 * A060212(n) - 1. - Sean A. Irvine, Oct 31 2022

Extensions

Offset changed to 1 by Michel Marcus, Dec 14 2013