A385124 Numbers k such that there are exactly 7 primes between 30*k and 30*k+30.

1, 2, 49, 62, 79, 89, 188, 6627, 9491, 18674, 22621, 31982, 34083, 38226, 38520, 41545, 48713, 53887, 89459, 103205, 114731, 123306, 139742, 140609, 149125, 168237, 175125, 210554, 223949, 229269, 237794, 240007, 267356, 288467, 321451, 364921, 368248, 373370, 391701

Offset: 1

Author

Jianglin Luo, Jun 18 2025

Keywords

• nonn

Comments

The count of primes in 30*k..30*k+30 is less than 8 for k >= 1.

It appears that this sequence has infinitely many terms.

Examples

			1 is a term since there are 7 primes in 30..60: 31, 37, 41, 43, 47, 53, 59.
2 is a term since there are 7 primes in 60..90: 61, 67, 71, 73, 79, 83, 89.
3 is not a term since there are only 6 primes in 90..120: 97, 101, 103, 107, 109, 113.
49 is a term since there are 7 primes in 30*49..30*50: 1471, 1481, 1483, 1487, 1489, 1493, 1499.
		

Links

• Jianglin Luo, Table of n, a(n) for n = 1..3500

Crossrefs

Union of A100418, A100419, A100420, A100421, A100422 and A100423.

Cf. A000720, A098592.

Programs

Mathematica

ArrayPlot[Table[Boole@PrimeQ[i*30+j],{i,0,399},{j,30}],Mesh->True]
index=1;Do[If[Length@(*PrimeRange=*) Select[Range[30*k+1,30*k+30,2],PrimeQ]==7,Print[index++," ",k]],{k,1,10^9}]

PARI

[n|n<-[1..10^6],#primes([30*n,30*n+30])==7]

Formula

{k | A098592(k) = pi(30*k+30) - pi(30*k) = 7}. - Michael S. Branicky, Jun 24 2025