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URL: https://oeis.org/A343404

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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).
3
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.
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), A360407 (related sequence).
Sequence in context: A006287 A087225 A366619 * A220182 A388339 A076064
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 14 2021
STATUS
approved