A305211 a(n) is the number of possible values of (x^3 + y^3) mod n, where x and y are any integers.

1, 2, 3, 4, 5, 6, 5, 8, 5, 10, 11, 12, 13, 10, 15, 16, 17, 10, 19, 20, 15, 22, 23, 24, 25, 26, 15, 20, 29, 30, 31, 32, 33, 34, 25, 20, 37, 38, 39, 40, 41, 30, 43, 44, 25, 46, 47, 48, 35, 50, 51, 52, 53, 30, 55, 40, 57, 58, 59, 60, 61, 62, 25, 64, 65, 66, 67

Offset

1,2

Comments

Conjecture: keyword mult applies. Furthermore a procedure to find a(n) is as follows: if n = 7k then n -> 5*n/7. if n = 9k then n-> 5*n/9. return(n). - David A. Corneth, May 22 2020

Links

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

Prog

(Python) [len(set((pow(x, 3, n)+pow(y, 3, n))%n for x in range(n) for y in range(x+1))) for n in range(1, 51)]
(PARI) a(n) = my(v=[]); for (x=1, n, for (y=1, n, v = concat(v, Mod(x, n)^3 + Mod(y, n)^3))); #Set(v); \\ Michel Marcus, Jul 10 2018
(PARI) a(n) = {my(v = Set(vector(n, i, i^3%n)), l); if(#v == n, return(n) , res = vector(n); for(i = 1, #v, for(j = i, #v, res[1 + (v[i] + v[j]) % n] = 1 ) ); vecsum(res) ) } \\ David A. Corneth, May 22 2020

Crossrefs

Cf. A155918 (with squares instead of cubes).

Sequence in context: A374478 A305900 A287943 * A091951 A063283 A228732

Adjacent sequences: A305208 A305209 A305210 * A305212 A305213 A305214

Keyword

nonn

Author

Jack Zhang, May 27 2018

Extensions

a(50)-a(67) from Jon E. Schoenfield, May 28 2018

Status

approved