

A305211


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


3



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
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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: A335130 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



