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The first number in A350578 to appear n times.
2

%I #15 Jan 09 2022 02:31:07

%S 0,42,153,504,921,921,17729,17729,17729,17729,60610,60610,109617,

%T 109617,109617,109617,109617,109617,109599,658778,658778,658778,

%U 658778,658778,658778,658778,658778,658778,658778,658778,658778,658778,658778,658778,658778,2184074,2184074,2184074

%N The first number in A350578 to appear n times.

%C See A350578 for further details.

%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>

%e a(1) = 0 as A350578(0) = 0, thus 0 is the first number to appear one time.

%e 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.

%e a(3) = 153 as A350578(74) = A350578(78) = A350578(114) = 153, thus 153 is the first number to appear three times.

%t 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];

%t Table[k=0;While[Max[Last/@(c=Tally@Array[a,++k,0])]!=i];a[k-1],{i,6}] (* _Giorgos Kalogeropoulos_, Jan 07 2022 *)

%o (Python)

%o from itertools import count

%o from collections import Counter

%o def A350579(n):

%o b, bcounter = 0, Counter({0})

%o for m in count(1):

%o if bcounter[b] == n: return b

%o b += -m if b-m >= 0 and bcounter[b-m] <= bcounter[b+m] else m

%o bcounter[b] += 1 # _Chai Wah Wu_, Jan 08 2022

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

%K nonn

%O 1,2

%A _Scott R. Shannon_, Jan 07 2022