A076947 -id:A076947 - cp's OEIS frontend

A091733 a(n) is the least m > 1 such that m^3 = 1 (mod n).

2, 3, 4, 5, 6, 7, 2, 9, 4, 11, 12, 13, 3, 9, 16, 17, 18, 7, 7, 21, 4, 23, 24, 25, 26, 3, 10, 9, 30, 31, 5, 33, 34, 35, 11, 13, 10, 7, 16, 41, 42, 25, 6, 45, 16, 47, 48, 49, 18, 51, 52, 9, 54, 19, 56, 9, 7, 59, 60, 61, 13, 5, 4, 65, 16, 67, 29, 69, 70, 11, 72, 25, 8, 47, 76, 45, 23, 55, 23

Offset: 1

David Wasserman, Mar 05 2004

a(n) <= n + 1; the inequality is strict iff n is divisible by 9 or by a prime congruent to 1 mod 3. - Robert Israel, May 27 2014

			a(7) = 2 because 2^3 is congruent to 1 (mod 7).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A070667, A076947, A083501.

m = 2; while mod(m^3 - 1, n); m = m + 1; end; m

A:= n -> min(select(t -> type((t^3-1)/n, integer), [$2 .. n+1]));
map(A, [$1 .. 1000]); # Robert Israel, May 27 2014

f[n_] := Block[{x = 2}, While[Mod[x^3 - 1, n] != 0, x++]; x]; Array[f, 79] (* Robert G. Wilson v, Mar 29 2016 *)

a(n) = my(k = 2); while(Mod(k, n)^3 != 1, k++); k; \\ Michel Marcus, Mar 30 2016

A266236 Least m > 0 such that m*n^3 + 1 is a cube.

Original entry on oeis.org

1, 7, 91, 37, 4291, 16003, 1801, 17, 263683, 19927, 1003003, 1775557, 111169, 506115, 17145, 423001, 16789507, 24152311, 1261657, 3266062, 64024003, 5080, 113411851, 148072393, 7082497, 244187503, 1922636, 14355469, 3132736, 594896491, 27009001, 8341522, 1073840131

Offset: 0

Alex Ratushnyak, Dec 25 2015

nonn

Least m>0 for which x^3 - m*y^3 = 1 has a solution with y = n.

			17*7^3+1 = 18^3, and 17 is the smallest positive m such that m*7^3+1 is a cube, so a(7)=17.

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Cf. A000578, A035096, A067872.

f[n_] := Block[{x = 2, n3 = n^3}, While[ Mod[x^3 - 1, n3] != 0, x++]; (x^3 - 1)/n3]; f[0] = 1; Array[f, 34, 0] (* Robert G. Wilson v, Mar 24 2016 *)

a(n) = {my(m = 1, cn = n^3); while (!ispower(m*cn + 1, 3), m++); m;} \\ Michel Marcus, Feb 09 2016

a(n) = A076947(n^3). - Robert Israel, Dec 25 2015

A076989 Smallest cube of the form n*k + 1 with k>0.

Original entry on oeis.org

8, 27, 64, 125, 216, 343, 8, 729, 64, 1331, 1728, 2197, 27, 729, 4096, 4913, 5832, 343, 343, 9261, 64, 12167, 13824, 15625, 17576, 27, 1000, 729, 27000, 29791, 125, 35937, 39304, 42875, 1331, 2197, 1000, 343, 4096, 68921, 74088, 15625, 216, 91125, 4096

Offset: 1

Amarnath Murthy, Oct 25 2002

			a(9) = 64 as 64 = 7*9 + 1.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A066498, A076947.

a[1] := 8:for n from 2 to 150 do j := 2:while((j^3 mod n)<>1)do j := j+1:od: a[n] := j^3:od:seq(a[k],k=1..150);
# Alternative
f:=proc(n) local R;
  R:= sort([numtheory:-rootsunity(3,n)] mod n);
  if nops(R)=1 then (n+1)^3 else R[2]^3 fi
end proc:
map(f, [$1..150]); # Robert Israel, Mar 30 2018

sc[n_]:=Module[{k=1},While[!IntegerQ[Surd[n*k+1,3]],k++];n*k+1]; Array[ sc,50] (* Harvey P. Dale, Mar 30 2018 *)

first(n) = my(res = vector(n)); {res[1] = 8; for(i = 2, n + 1, i3 = i ^ 3-1; d = divisors(i3); j = 2; while(j <= #d && d[j] <= n, if(res[d[j]] == 0, res[d[j]] = i3 + 1); j++)); res} \\ David A. Corneth, Mar 30 2018

a(n) <= (n+1)^3. In particular, a(n) < (n+1)^3 if n is in A066498. - David A. Corneth, Mar 30 2018

a(n) = A076947(n)*n + 1. - Altug Alkan, Mar 30 2018

More terms from Sascha Kurz, Jan 26 2003

cp's OEIS Frontend

A091733 a(n) is the least m > 1 such that m^3 = 1 (mod n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

MATLAB

Maple

Mathematica

PARI

A266236 Least m > 0 such that m*n^3 + 1 is a cube.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A076989 Smallest cube of the form n*k + 1 with k>0.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions