A350579 The first number in A350578 to appear n times.

0, 42, 153, 504, 921, 921, 17729, 17729, 17729, 17729, 60610, 60610, 109617, 109617, 109617, 109617, 109617, 109617, 109599, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 658778, 2184074, 2184074, 2184074

Offset

1,2

Comments

See A350578 for further details.

Links

Table of n, a(n) for n=1..38.

Index entries for sequences related to Recamán's sequence

Example

a(1) = 0 as A350578(0) = 0, thus 0 is the first number to appear one time.
a(2) = 42 as A350578(20) = A350578(24) = 42, thus 42 is the first number to appear two times. This is also true for A005132.
a(3) = 153 as A350578(74) = A350578(78) = A350578(114) = 153, thus 153 is the first number to appear three times.

Mathematica

a[0]=0; a[n_]:=a[n]=If[a[n-1]-n>=0&&Count[Array[a, n-1, 0], a[n-1]-n]<=Count[Array[a, n-1, 0], a[n-1]+n], a[n-1]-n, a[n-1]+n];
Table[k=0; While[Max[Last/@(c=Tally@Array[a, ++k, 0])]!=i]; a[k-1], {i, 6}] (* Giorgos Kalogeropoulos, Jan 07 2022 *)

Prog

(Python)
from itertools import count
from collections import Counter
def A350579(n):
    b, bcounter = 0, Counter({0})
    for m in count(1):
        if bcounter[b] == n: return b
        b += -m if b-m >= 0 and bcounter[b-m] <= bcounter[b+m] else m
        bcounter[b] += 1 # Chai Wah Wu, Jan 08 2022

Crossrefs

Cf. A350578, A005132, A335299, A064389, A261573, A064387.

Sequence in context: A158479 A188126 A189500 * A075289 A193571 A326384

Adjacent sequences: A350576 A350577 A350578 * A350580 A350581 A350582

Keyword

nonn

Author

Scott R. Shannon, Jan 07 2022

Status

approved