A109562 prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 8.

293, 1069, 1259, 1637, 2311, 2557, 3229, 3469, 3739, 3967, 4027, 4177, 4523, 4759, 5237, 6173, 6397, 6737, 7079, 7369, 7793, 8123, 8329, 9067, 11213, 11551, 12011, 12347, 13339, 14563, 14593, 14897, 16273, 16843, 18013, 18919, 20563, 21031, 21283, 21347, 21529

Offset: 1

Author

Roger L. Bagula, Jun 27 2005

Keywords

• nonn
• less

Crossrefs

Cf. A000040, A000720, A001359.

Cf. A109556-A109569 for m = 2..15.

Programs

Mathematica

a = Flatten[Table[If[Floor[2*Mod[(Prime[n + 1] - Prime[n])*PrimePi[n]/n, 8]] == 8, Prime[n], {}], {n, 1, 400}]]

Extensions

Name edited, offset corrected and more terms added by Amiram Eldar, Jun 02 2025