A051853 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.

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, 1, 1541

Offset

1,3

Links

Table of n, a(n) for n=1..61.

Formula

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

Example

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;

Maple

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;
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;
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;

Mathematica

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 *)

Crossrefs

Cf. A051854.

Sequence in context: A323359 A324036 A075677 * A159074 A147414 A117637

Adjacent sequences: A051850 A051851 A051852 * A051854 A051855 A051856

Keyword

nonn,tabf

Author

Antti Karttunen, Dec 13 1999

Status

approved