A279086 Number of distinct residues n mod p encountered before the first repeated residue as p runs through the primes.

1, 2, 3, 3, 4, 1, 1, 5, 5, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2, 2, 3, 3, 1, 1, 5, 5, 3, 3, 1, 1, 2, 4, 4, 3, 1, 1, 3, 3, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2, 2, 5, 5, 1, 1, 3, 3, 4, 4, 1, 1, 2, 3, 3, 3, 1, 1, 4, 5, 2, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2, 2, 4, 4, 1, 1, 3, 6

Offset: 1

Author

Jon E. Schoenfield, Jan 15 2017

Keywords

• nonn

Comments

A279073(j) = min_{n : a(n) >= j}.

A279074(j) = min_{n : a(n) = j}.

Examples

			For n=11, the residues n mod prime(j) for j>=1 begin with 11 mod 2 = 1, 11 mod 3 = 2, and 11 mod 5 = 1; the first 2 residues are distinct, but the 3rd is a repeat of an earlier one, so a(11) = 2.
For n=87, the residues n mod prime(j) for j>=1 begin with 87 mod 2 = 1, 87 mod 3 = 0, 87 mod 5 = 2, 87 mod 7 = 3, 87 mod 11 = 10, 87 mod 13 = 9, 87 mod 17 = 2; the first 6 residues are all distinct, but the 7th is a repeat (87 mod 17 = 87 mod 5 = 2), so a(87) = 6.
		

Crossrefs

Cf. A279073, A279074.