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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
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.
Sequence in context: A222127 A221999 A222334 * A181948 A238943 A070081
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Jan 17 2021
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)