A249727 Start with a(1) = 1; then numbers 1 .. primepi(2), followed by numbers 1 .. primepi(3), and then numbers 1 .. primepi(4), ..., etc, where A000720 gives primepi.

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

Offset

1,4

Comments

Can be used to construct the irregular table A249809.

This is a fractal sequence; i.e., the removal of the first occurrence of each term in A249727 leaves A249727, so that the sequence contains itself infinitely many times. The corresponding interspersion is A272616. - Clark Kimberling, May 12 2016

Links

Antti Karttunen, Table of n, a(n) for n = 1..10016

Mathematica

Flatten[Table[Range[PrimePi[n]], {n, 2, 100}]]
(* Clark Kimberling, May 14 2016 *)

Prog

(Scheme) (define (A249727 n) (if (= 1 n) 1 (- n (+ 1 (A046992 (- (A249728 n) 1))))))

Crossrefs

Cf. A000720, A046992, A249728, A249809, A272616.

Sequence in context: A121997 A023128 A237260 * A023118 A122197 A030718

Adjacent sequences: A249724 A249725 A249726 * A249728 A249729 A249730

Keyword

nonn

Author

Antti Karttunen, Nov 06 2014

Status

approved