A077038 Least difference of primes p, q such that p < n^3 < q.

4, 6, 6, 14, 12, 10, 12, 6, 12, 34, 10, 24, 8, 16, 6, 10, 12, 6, 16, 20, 12, 34, 22, 10, 6, 6, 18, 12, 18, 14, 22, 18, 12, 36, 14, 20, 8, 52, 10, 10, 16, 38, 34, 6, 40, 24, 10, 16, 12, 14, 8, 18, 20, 30, 20, 32, 18, 34, 40, 48, 10, 6, 8, 18, 10, 18, 18, 30, 30, 30, 42, 20, 6, 44

Offset: 2

Author

Reinhard Zumkeller, Oct 21 2002

Keywords

• nonn

Comments

Least m such that a(m)=2*n for n=1,2,3,... are: {2,3,14,7,6,5,15,28,21,24,13,...}. - Zak Seidov, May 10 2016

There are numbers k other than 2 such that a(k) = 4. The first few (up to 1000) are 129 189 369 435 549 555 561 819. Conjecture: every even integer greater than 2 occurs infinitely often in this sequence. - Franklin T. Adams-Watters, May 13 2016

Links

• Zak Seidov, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A058043, A000578.

Programs

Mathematica

Table[c=n^3;NextPrime[c]-NextPrime[c,-1],{n,2,80}] (* Harvey P. Dale, Sep 14 2012 *)

Formula

a(n) = A014220(n) - A077037(n).