

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
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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 (* JeanFrançois 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



