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 A385124 #40 Jun 24 2025 15:33:50
%S A385124 1,2,49,62,79,89,188,6627,9491,18674,22621,31982,34083,38226,38520,
%T A385124 41545,48713,53887,89459,103205,114731,123306,139742,140609,149125,
%U A385124 168237,175125,210554,223949,229269,237794,240007,267356,288467,321451,364921,368248,373370,391701
%N A385124 Numbers k such that there are exactly 7 primes between 30*k and 30*k+30.
%C A385124 The count of primes in 30*k..30*k+30 is less than 8 for k >= 1.
%C A385124 It appears that this sequence has infinitely many terms.
%H A385124 Jianglin Luo, <a href="/A385124/b385124.txt">Table of n, a(n) for n = 1..3500</a>
%F A385124 {k | A098592(k) = pi(30*k+30) - pi(30*k) = 7}. - _Michael S. Branicky_, Jun 24 2025
%e A385124 1 is a term since there are 7 primes in 30..60: 31, 37, 41, 43, 47, 53, 59.
%e A385124 2 is a term since there are 7 primes in 60..90: 61, 67, 71, 73, 79, 83, 89.
%e A385124 3 is not a term since there are only 6 primes in 90..120: 97, 101, 103, 107, 109, 113.
%e A385124 49 is a term since there are 7 primes in 30*49..30*50: 1471, 1481, 1483, 1487, 1489, 1493, 1499.
%t A385124 ArrayPlot[Table[Boole@PrimeQ[i*30+j],{i,0,399},{j,30}],Mesh->True]
%t A385124 index=1;Do[If[Length@(*PrimeRange=*) Select[Range[30*k+1,30*k+30,2],PrimeQ]==7,Print[index++," ",k]],{k,1,10^9}]
%o A385124 (PARI) [n|n<-[1..10^6],#primes([30*n,30*n+30])==7]
%Y A385124 Union of A100418, A100419, A100420, A100421, A100422 and A100423.
%Y A385124 Cf. A000720, A098592.
%K A385124 nonn
%O A385124 1,2
%A A385124 _Jianglin Luo_, Jun 18 2025