This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
is(n)=n%2 && Mod(2, 2*n-1)^n==1
1 is in this sequence because (2^1 + 1)/(2*1 + 1) = 1, 2 is in this sequence because (2^0 + 1)/(2*0 + 1) = 2, 3 is in this sequence because (2^5 + 1)/(2*5 + 1) = 3.
s=[]; for(k=0, 100, t=(2^k + 1)/(2*k + 1); if(type(t)=="t_INT", s=concat(s, t))); s=vecsort(s,,8) \\ Colin Barker, Nov 18 2014
[n: n in [1..200000] | Modexp(3, n, 3*n-1) eq 1];
a:= proc(n) option remember; local k;
if n=1 then 1 else for k from 1+a(n-1)
while 3&^k mod(3*k-1)<>1 do od; k fi
end:
seq(a(n), n=1..40); # Alois P. Heinz, May 27 2016
Select[Range[10^6], PowerMod[3, #, 3*# - 1] == 1 &] (* Giovanni Resta, May 27 2016 *)
is(n)=Mod(3,3*n-1)^n==1 \\ Charles R Greathouse IV, May 29 2016
2^8-1=255 is divisible by 2*8-1=15 and by 2*8+1=17.
Select[Range[23*10^5],PowerMod[2,#,2#+{1,-1}]=={1,1}&] (* Harvey P. Dale, Dec 19 2014 *)
isok(n) = !((2^n-1) % (2*n-1)) && !((2^n-1) % (2*n+1));
is(n)=Mod(2,4*n^2-1)^n==1 \\ Charles R Greathouse IV, Dec 04 2013
1 is in this sequence because (2^1 + 1)/(2*1 - 1) = 3.
[n: n in [1..2000000] | Denominator((2^n + 1)/(2*n - 1)) eq 1];
Select[Range[200000], IntegerQ[(2^# + 1) / (2 # - 1)] &] (* Vincenzo Librandi, Nov 20 2014 *)
is(n)=Mod(2,2*n-1)^n==-1 \\ Charles R Greathouse IV, Nov 20 2014
n = 1: (2^k - 1) mod (1*k - 1) = 0 is true for least k = 2, thus a(1) = 2. n = 3: (2^k - 1) mod (3*k - 1) = 0 is true for least k = 12, thus a(3) = 12.
f:= proc(n) local k;
for k from 2 by (n mod 2 + 1) do if 2 &^k - 1 mod (n*k-1) = 0 then return k fi od
end proc:
map(f, [$1..200]); # Robert Israel, Mar 12 2025
a[n_] := Module[{k = 2}, While[n*k-1 != 1 && PowerMod[2, k, n*k-1] != 1, k++]; k]; Array[a, 50] (* Amiram Eldar, Mar 10 2025 *)
a(n) = my(k=2); while (Mod(2, n*k-1)^k != 1, k++); k; \\ Michel Marcus, Mar 10 2025
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