OFFSET
1,1
COMMENTS
Numbers m such that the base-6 representation of (5*m-3) starts with 11 or 12 or 13 or 14 or 15 or ends with 0.
First differences give a run of 6^i 1's followed by a run of 6^i 6's, for i >= 0.
LINKS
FORMULA
For n in the range (2*6^i + 3)/5 <= n < (7*6^i + 3)/5, for i >= 0:
a(n) = n + 6^i.
a(n+1) = 1 + a(n).
Otherwise, for n in the range (7*6^i + 3)/5 <= n < (12*6^i + 3)/5, for i >= 0:
a(n) = 6*(n - 6^i) - 3.
a(n+1) = 6 + a(n).
EXAMPLE
a(5) = 11 because (2*6^1 + 3)/3 <= 5 < (7*6^1 + 3)/5, hence a(5) = 5 + 6^1 = 11;
a(10) = 21 because (7*6^1 + 3)/5 <= 10 < (12*6^1 + 3)/5, hence a(10) = 6*(10 - 6^1) - 3 = 21.
MATHEMATICA
okQ[m_] := With[{id = IntegerDigits[5 m - 3, 6] }, MatchQ[id[[1 ;; 2]], {1, 1}|{1, 2}|{1, 3}|{1, 4}|{1, 5}] || id[[-1]] == 0];
Join[{2}, Select[Range[3, 1000], okQ]] (* Jean-François Alcover, Sep 22 2023 *)
PROG
(C++)
/* program used to generate the b-file */
#include<iostream>
using namespace std;
int main(){
int cnt1=1, flag=0, cnt2=1, a=2;
for(int n=1; n<=10000; n++) {
cout<<n<<" "<<a<<endl;
if(cnt2==cnt1) {
flag=1-flag;
cnt1=1;
if(flag) a+=1;
else {
a+=6;
cnt2*=6;
}
}
else {
cnt1++;
a+=(flag?6:1);
}
}
return 0;
}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yifan Xie, Jul 15 2022
STATUS
approved