A343404 For any number n with representation (d_w, ..., d_1) in primorial base, a(n) is the least number m such that m mod prime(k) = d_k for k = 1..w (where prime(k) denotes the k-th prime number).

0, 1, 4, 1, 2, 5, 6, 21, 16, 1, 26, 11, 12, 27, 22, 7, 2, 17, 18, 3, 28, 13, 8, 23, 24, 9, 4, 19, 14, 29, 120, 15, 190, 85, 50, 155, 36, 141, 106, 1, 176, 71, 162, 57, 22, 127, 92, 197, 78, 183, 148, 43, 8, 113, 204, 99, 64, 169, 134, 29, 30, 135, 100, 205

Offset

0,3

Comments

Leading zeros in primorial base expansions are ignored.

The Chinese remainder theorem ensures that this sequence is well defined and provides a way to compute it.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Wikipedia, Chinese remainder theorem

Index entries for sequences related to primorial base

Formula

a(n) = 1 iff n belongs to A143293.

a(n) = n iff n belongs to A343405.

a(n) < A002110(k) for any n < A002110(k) and k >= 0.

a(A002110(k)) = A079276(k+1) * A002110(k) for any k >= 0.

Example

For n = 42 :
- the expansion of 42 in primary base is "1200",
- so a(42) mod 2 = 0 => a(42) = 2*t for some t >= 0,
     a(42) mod 3 = 0 => a(42) = 6*u for some u >= 0,
     a(42) mod 5 = 2 => a(42) = 12 + 30*v for some v >= 0,
     a(42) mod 7 = 1 => a(42) = 162 + 210*w for some w >= 0,
- we choose w=0 so as to minimize the value,
- hence a(42) = 162.

Prog

(PARI) a(n) = { my (v=Mod(0, 1)); forprime (p=2, oo, if (n==0, return (lift(v)), v=chinese(v, Mod(n, p)); n\=p)) }

Crossrefs

Cf. A002110, A079276, A143293, A235168, A343405 (fixed points).

Sequence in context: A006287 A087225 A366619 * A220182 A076064 A293570

Adjacent sequences: A343401 A343402 A343403 * A343405 A343406 A343407

Keyword

nonn,base

Author

Rémy Sigrist, Apr 14 2021

Status

approved