A022447 Fractal sequence of the dispersion of the primes.

1, 1, 1, 2, 1, 3, 2, 4, 5, 6, 1, 7, 3, 8, 9, 10, 2, 11, 4, 12, 13, 14, 5, 15, 16, 17, 18, 19, 6, 20, 1, 21, 22, 23, 24, 25, 7, 26, 27, 28, 3, 29, 8, 30, 31, 32, 9, 33, 34, 35, 36, 37, 10, 38, 39, 40, 41, 42, 2, 43, 11, 44, 45, 46, 47, 48, 4, 49, 50, 51, 12, 52, 13, 53, 54, 55, 56, 57, 14

Offset

1,4

References

C. Kimberling, Fractal sequences and interspersions, Ars Combinatoria, vol. 45, p. 157, 1997.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Sean A. Irvine, Java program (github)

C. Kimberling, Interspersions

Example

From Sean A. Irvine, May 20 2019: (Start)
The prime counting function, pi(n), is iterated (possibly zero times) until a nonprime is reached.  If the result of this iteration is m, then a(n) = m - pi(m).  Examples:
n=11: pi(11)=5, pi(5)=3, pi(3)=2, pi(2)=1. Hence, m=1 and so a(11) = 1-pi(1) = 1.
n=12: is already nonprime, hence m=12 and so a(12) = 12-pi(12) = 7.
n=13: pi(13)=6 (a nonprime), hence m=6 and so a(13) = 6-pi(6) = 3.
(End)

Mathematica

m = 30; list = Table[Length[NestWhileList[PrimePi, n, PrimeQ]], {n, m}]; Table[Length@Position[Take[list, k], list[[k]]], {k, Length[list]}] (* Birkas Gyorgy, Apr 04 2011 *)
primefractal[n_]:= (# - PrimePi[#]) &@NestWhile[PrimePi, n, PrimeQ]; Array[primefractal, 30] (* Birkas Gyorgy, Apr 04 2011 *)

Crossrefs

Cf. A000720, A022446, A114537, A114538, A114577.

Sequence in context: A227859 A026272 A193564 * A117194 A340647 A318746

Adjacent sequences: A022444 A022445 A022446 * A022448 A022449 A022450

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(67) onward added by G. C. Greubel, Feb 28 2018

Offset corrected by Sean A. Irvine, May 20 2019

Status

approved