A109558 prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 4.

7, 13, 19, 47, 53, 61, 73, 83, 131, 359, 389, 401, 449, 479, 491, 691, 709, 787, 811, 829, 919, 1021, 1039, 1051, 1153, 1171, 1249, 1399, 1471, 1627, 1699, 1723, 1801, 1879, 2017, 2029, 2053, 2069, 2089, 2099, 2143, 2297, 2399, 2447, 2579, 2621

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]] == 4, Prime[n], {}], {n, 1, 400}]]

Extensions

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