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

Author

Antti Karttunen, Nov 06 2014

Keywords

• nonn

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

Crossrefs

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

Programs

Mathematica

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

Scheme

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