This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060213 #31 Oct 31 2022 19:26:01 %S A060213 11,17,29,41,101,137,281,617,641,821,1697,1877,2081,2237,2381,2657, %T A060213 2801,3461,3557,3917,4637,4721,5441,6197,6701,8537,8597,9677,10937, %U A060213 12161,12377,12821,12917,13217,13721,13757,13997,14081,16061,17417 %N A060213 Lesser of twin primes whose average is 6 times a prime. %C A060213 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 %H A060213 Harvey P. Dale, <a href="/A060213/b060213.txt">Table of n, a(n) for n = 1..1000</a> %H A060213 Lubomir Alexandrov, <a href="https://arxiv.org/abs/math/9811096">On the nonasymptotic prime number distribution</a>, arXiv:math/9811096 [math.NT], 1998, see p. 15. %F A060213 a(n) = 6 * A060212(n) - 1. - _Sean A. Irvine_, Oct 31 2022 %e A060213 102197 is here because 102198 = 17033*6 and 17033 is prime. %p A060213 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)])); %t A060213 Transpose[Select[Partition[Prime[Range[2500]],2,1],#[[2]]-#[[1]] == 2 && PrimeQ[Mean[#]/6]&]][[1]] (* _Harvey P. Dale_, May 04 2014 *) %o A060213 (PARI) isok(n) = isprime(n) && isprime(n+2) && !((n+1) % 6) && isprime((n+1)/6); \\ _Michel Marcus_, Dec 14 2013 %Y A060213 Cf. A002822, A058383, A059960, A027856, A001454, A001359, A060212. %K A060213 nonn %O A060213 1,1 %A A060213 _Labos Elemer_, Mar 20 2001 %E A060213 Offset changed to 1 by _Michel Marcus_, Dec 14 2013