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A191228 Greatest Ramanujan prime index less than x, eta(x). 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 4 03:18 EDT 2021. Contains 346442 sequences. (Running on oeis4.)