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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 19 20:58 EDT 2024. Contains 374436 sequences. (Running on oeis4.)