A178216 a(n) = prime(A178215(n)) mod prime(n).

1, 1, 4, 1, 10, 12, 1, 1, 22, 27, 1, 32, 10, 33, 27, 24, 1, 24, 8, 48, 72, 55, 39, 69, 44, 22, 16, 105, 44, 56, 14, 76, 87, 129, 22, 138, 85, 50, 82, 130, 69, 93, 18, 60, 135, 170, 105, 110, 225, 44

Offset

1,3

Comments

a(n) is the last residue modulo prime(n) in the minimal set of the first primes which contains all residues modulo prime(n).

Build the smallest set {prime(1), prime(2), ..., prime(k)} of the first k consecutive primes such that the set {prime(1) mod prime(n), prime(2) mod prime(n), ..., prime(k) mod prime(n)} contains all residues {0, 1, 2, ..., prime(n)-1}. Then a(n) = prime(k) mod prime(n). - R. J. Mathar, Oct 25 2010

Links

Table of n, a(n) for n=1..50.

Example

If n=3, then prime(n)=5 and {2,3,5,7,11,13,17,19} is the minimal set of the first primes which contains all residues modulo 5. We have consecutive residues {2,3,0,2,1,3,2,4}. Therefore a(3)=4.

Maple

A178216 := proc(n) local p, k, modP, i ; p := ithprime(n) ; for k from 1 do modP := [seq( ithprime(j) mod p, j=1..k)] ; {seq(i, i=0..p-1)} minus convert(modP, set) ; if % = {} then return op(-1, modP) ; end if; end do: end proc: seq(A178216(n), n=1..50) ; # R. J. Mathar, Oct 25 2010

Crossrefs

Cf. A000040, A178215.

Sequence in context: A349809 A182971 A062145 * A307529 A019213 A019128

Adjacent sequences: A178213 A178214 A178215 * A178217 A178218 A178219

Keyword

nonn

Author

Vladimir Shevelev, May 22 2010

Extensions

a(10) corrected, more terms appended by R. J. Mathar, Oct 25 2010

Name corrected by Jon E. Schoenfield, May 10 2019

Status

approved