A114961 Numbers n such that PrimePi(prime(n + 1)^2) - PrimePi(prime(n)^2) < c*n with c=9/5.

7, 10, 13, 20, 26, 28, 33, 35, 43, 45, 49, 52, 57, 60, 64, 89, 98, 109, 113, 116, 120, 140, 142, 144, 148, 152, 171, 173, 176, 178, 182, 190, 201, 209, 212, 215, 225, 230, 234, 236, 253, 256, 262, 265, 268, 277, 286, 288, 294, 296, 302, 307, 313, 315, 318, 320

Offset: 1

Author

Robert G. Wilson v, Feb 21 2006

Keywords

• nonn

Comments

If c=2 instead of 1.8 then the sequence is A029707.

This sequence is probably finite with 699 terms with 14020 being the last.

If c=1.7 the sequence is just {7, 10, 13, 20, 26, 28, 33, 35, 45, 49, 57, 60, 64, 89, 98, 109, 113, 116, 171, 190, 201, 215, 225, 234, 236, 256, 288, 332, 384, 405, 430, 486, 495, 498, 524, 530, 601, 613, 625, 872}.

If c=1.6 the sequence is just {7, 13, 20, 28, 33, 57, 109}.

If c=3/2 the sequence has but one term, 33.

References

• P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, NY, 1995, page 248.

Crossrefs

Cf. A029707.

Programs

Mathematica

t = {}; Do[ If[ PrimePi[ Prime[n + 1]^2] - PrimePi[ Prime[n]^2] < 9n/5, AppendTo[t, n]], {n, 10^5}]; t