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A340716 Lexicographically earliest sequence of positive integers with as many distinct values as possible such that for any n > 0, a(n + pi(n)) = a(n) (where pi(n) = A000720(n) corresponds to the number of prime numbers <= n). 2
1, 2, 2, 3, 2, 3, 4, 2, 3, 5, 4, 2, 3, 5, 6, 4, 2, 7, 3, 5, 6, 4, 8, 2, 7, 9, 3, 5, 6, 4, 10, 8, 2, 7, 9, 3, 5, 11, 6, 4, 12, 10, 8, 2, 7, 9, 3, 13, 5, 11, 6, 4, 14, 12, 10, 15, 8, 2, 7, 9, 16, 3, 13, 5, 11, 6, 4, 17, 14, 12, 10, 15, 8, 2, 18, 7, 9, 19, 16, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The condition "with as many distinct values as possible" means here that for any distinct m and n, provided the orbits of m and n under the map x -> x + pi(x) do not merge, then a(m) <> a(n).

This sequence has similarities with A003602 (A003602(2*n) = A003602(n)) and with A163491 (A163491(n+ceiling(n/2)) = A163491(n)).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 2 iff n belongs to A061535.

a(A095116(n)) = n + 1.

EXAMPLE

The first terms, alongside n + pi(n), are:

  n   a(n)  n + pi(n)

  --  ----  ---------

   1     1          1

   2     2          3

   3     2          5

   4     3          6

   5     2          8

   6     3          9

   7     4         11

   8     2         12

   9     3         13

  10     5         14

  11     4         16

  12     2         17

PROG

(PARI) u=0; for (n=1, #a=vector(80), if (a[n]==0, a[n]=u++); print1 (a[n]", "); m=n+primepi(n); if (m<=#a, a[m]=a[n]))

CROSSREFS

See A003602, A163491 and A340717 for similar sequences.

Cf. A000720, A095117.

Sequence in context: A222127 A221999 A222334 * A181948 A238943 A070081

Adjacent sequences:  A340713 A340714 A340715 * A340717 A340718 A340719

KEYWORD

nonn,look

AUTHOR

Rémy Sigrist, Jan 17 2021

STATUS

approved

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Last modified September 24 18:11 EDT 2022. Contains 356949 sequences. (Running on oeis4.)