cp's OEIS Frontend

A340573 a(n) is the smallest lesser twin prime p from A001359 such that the distance to the previous lesser twin prime is 6*n.

%I A340573 #29 Dec 18 2021 11:18:21
%S A340573 11,29,59,641,101,347,2309,569,1931,521,1787,419,1229,1871,3671,2237,
%T A340573 6551,1427,21491,1607,12377,4931,1019,23201,809,19697,12539,2549,
%U A340573 38921,10709,37547,8819,9239,34031,6089,80447,15581,46049,36341,14867,38237,36779,87509,71261,15137,40427,13679,54917,41141,50891
%N A340573 a(n) is the smallest lesser twin prime p from A001359 such that the distance to the previous lesser twin prime is 6*n.
%C A340573 Lesser twin primes (with the exception of prime 3) are congruent to 5 modulo 6, which implies that distances between successive pairs of twin primes are 6*k.
%H A340573 Martin Raab, <a href="/A340573/b340573.txt">Table of n, a(n) for n = 1..4508</a>
%F A340573 a(n) = A052350(n) + 6*n.
%e A340573 a(1)=11 because 11 - 5 = 6*1.
%e A340573 a(2)=41 because 41 - 29 = 6*2.
%e A340573 a(3)=59 because 59 - 41 = 6*3.
%t A340573 Table[a[n] = 0, {n, 1, 10000}]; Table[
%t A340573 b[n] = 0, {n, 1, 10000}]; qq = {}; prev = 5; Do[
%t A340573 If[Prime[n + 1] - Prime[n] == 2, k = (Prime[n] - prev)/6;
%t A340573   If[b[k] == 0, a[k] = Prime[n]; b[k] = 1]; prev = Prime[n]], {n, 5,
%t A340573   10000}]; list = Table[a[n], {n, 1, 50}]
%t A340573 (* Second program: *)
%t A340573 pp = Select[Prime[Range[10^4]], PrimeQ[#+2]&];
%t A340573 dd = Differences[pp];
%t A340573 a[n_] := pp[[FirstPosition[dd, 6n][[1]]+1]];
%t A340573 Array[a, 50] (* _Jean-François Alcover_, Jan 13 2021 *)
%Y A340573 Cf. A001359, A001359, A053319, A007530, A052380, A052381, A113274, A113275, A052350.
%K A340573 nonn
%O A340573 1,1
%A A340573 _Artur Jasinski_, Jan 12 2021