A051854 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 rightmost a (an) varying fastest.

1, 1, 5, 1, 7, 13, 19, 11, 17, 23, 29, 1, 121, 31, 151, 61, 181, 127, 37, 157, 67, 187, 97, 43, 163, 73, 193, 103, 13, 169, 79, 199, 109, 19, 139, 71, 191, 101, 11, 131, 41, 197, 107, 17, 137, 47, 167, 113, 23, 143, 53, 173, 83, 29, 149, 59, 179, 89, 209, 1, 211, 421

Offset

1,3

Links

Table of n, a(n) for n=1..62.

Formula

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

Example

Rows have lengths 1,2,8,48,480,5760,92160,... (A005867(n)) and terms 1; 1,5; 1,7,13,19,11,17,23,29;

Maple

with(numtheory); incr_plist_from_right := proc(aa) local i, n, a; a := aa; n := nops(a); for i from n by -1 to 1 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_right_n_times := proc(aa, n) local a, i; a := aa; for i from 1 to n do a := incr_plist_from_right(a); od; RETURN(a); end; prim_chrem_right := proc(n) local r, m; r := incr_plist_from_right_n_times([], n); m := form_modlist(r); RETURN(chrem(r, m)); end; # For form_modlist see A051853.

Mathematica

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

Crossrefs

Cf. A051853.

Sequence in context: A233091 A286941 A332459 * A006569 A224139 A320905

Adjacent sequences: A051851 A051852 A051853 * A051855 A051856 A051857

Keyword

nonn,tabf

Author

Antti Karttunen, Dec 13 1999

Status

approved