A051853 - OEIS

%I #8 Mar 06 2016 10:54:32

%S 1,1,5,1,11,7,17,13,23,19,29,1,71,127,197,43,113,169,29,121,191,37,

%T 107,163,23,79,149,31,101,157,17,73,143,199,59,151,11,67,137,193,53,

%U 109,179,61,131,187,47,103,173,19,89,181,41,97,167,13,83,139,209,1,1541

%N Table of solutions to all possible Chinese Remainder Equations x = a1 mod p1, x = a2 mod p2, ..., x = an mod pn, where p1 - pn are the first n primes and each a1 - an varies between 1 and (its respective) p-1, with the leftmost a varying fastest.

%F a(n) = prim_chrem_left(n) (see Maple code)

%e Rows have lengths 1,2,8,48,480,5760,92160,... (A005867(n)) and terms 1; 1,5; 1,11,7,17,13,23,19,29; 1,71,127,197,43,113,169,29,121,191,37,107,163,23,79,149,31,101,157,17,73,143,199,59,151,11,67,137,193,53,109,179,61,131,187,47,103,173,19,89,181,41,97,167,13,83,139,209;

%p with(numtheory); incr_plist_from_left := proc(aa) local i,n,a; a := aa; n := nops(a); for i from 1 to n do if(a[i] < (ithprime(i)-1)) then a[i] := a[i]+1; RETURN(a); else a[i] := 1; fi; od; RETURN([op(a),1]); end;

%p incr_plist_from_left_n_times := proc(aa,n) local a,i; a := aa; for i from 1 to n do a := incr_plist_from_left(a); od; RETURN(a); end; form_modlist := proc(a) local b,i; b := []; for i from 1 to nops(a) do b := [op(b),ithprime(i)]; od; RETURN(b); end;

%p prim_chrem_left := proc(n) local r,m; r := incr_plist_from_left_n_times([],n); m := form_modlist(r); RETURN(chrem(r,m)); end;

%t row[n_] := Module[{i}, pp = Prime[Range[n]]; iter = Sequence @@ Table[{i[k], 1, pp[[k]] - 1}, {k, n, 1, -1}]; Table[ChineseRemainder[Array[i, n], pp], iter // Evaluate] // Flatten]; Table[row[n], {n, 1, 5}] // Flatten (* _Jean-François Alcover_, Mar 06 2016 *)

%Y Cf. A051854.

%K nonn,tabf

%O 1,3

%A _Antti Karttunen_, Dec 13 1999