A051853 -id:A051853 - cp's OEIS frontend

A083235 First differences of A063742, the possible values for cototients.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Labos Elemer, May 20 2003

nonn

Differences between consecutive numbers in the range of A051853.

			First missing number in A063742 is 10=A005278[1], so a[10]=2 is the first difference here > 1.

t0[x_] := Table[j, {j, 1, x}] t=Table[w-EulerPhi[w], {w, 1, 10000}]; u=Union[%]; Delete[u-RotateRight[u], 1]

a(n) = A063742(n+1) - A063742(n).

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 23 2007

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.

Original entry on oeis.org

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

Antti Karttunen, Dec 13 1999

			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;

Cf. A051853.

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.

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 *)

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

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A083235 First differences of A063742, the possible values for cototients.

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