A191228 Greatest Ramanujan prime index less than x, eta(x).

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10

Offset

1,11

Comments

a(n) is the greatest value k of A104272(k) less than x. The integer inverse function of A104272.

Starting at index m = a(A174602(n)) in A190874(m), the first instance of a count of n - 1 consecutive 1's is seen.

Links

Table of n, a(n) for n=1..100.

J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.

Example

a(17) = eta(17) = 3. Or, R_3 = 17.

Mathematica

nn = 100; R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s + 1]] = k], {k, Prime[3 nn]}];
A104272 = R + 1;
Table[Boole[MemberQ[A104272, k]], {k, 1, 100}] // Accumulate (* Jean-François Alcover, Nov 07 2018, using T. D. Noe's code for A104272 *)

Crossrefs

Cf. A104272, A191225, A191226, A191227.

Sequence in context: A099396 A126235 A220104 * A340763 A286103 A056556

Adjacent sequences: A191225 A191226 A191227 * A191229 A191230 A191231

Keyword

nonn

Author

John W. Nicholson, May 28 2011

Status

approved