This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
For n=5, a(5) = (A060371(5) - A094998(5))/A056604(5) = (3628801 - 25201)/27720 = 130.
[(Factorial(p-1)+1-Modinv(p,Lcm([1..p-1]))*p)/Lcm([1..p]): p in PrimesUpTo(50)];
with(numtheory): P:=proc(q) local a,j,k,ok,n; print(1); a:=[1]; for n from 3 to q do k:=0; a:=[op(a),n]; if isprime(n) then ok:=0; while ok=0 do ok:=1; k:=k+1; for j from 2 to n-1 do if not (k*n mod j)=1 then ok:=0; break; fi; od; od; print((((n-1)!+1)-k*n)/lcm(op(a))); fi; od; end: P(100); # Paolo P. Lava, Feb 16 2015
r[k_] := LCM @@ Range[k]; s[k_] := PowerMod[k, -1, r[k - 1]] k; w[k_] := ((k - 1)! + 1 - s[k])/r[k]; Table[w[Prime[n]], {n, 1, 20}]
For n = 7, prime(7) = 17, using the alternative definition (see Comment), a(7) = 2^4*3^2*5^1*7^1*11^1*13^1 = 16*9*5*7*11*13 = 720720 = 24*30030 = 2^2*6*30030 = A002110(1)^2*A002110(2)*A002110(6). - _David James Sycamore_, Oct 24 2024
[Lcm([2..p-1]): p in PrimesUpTo(70)]; // Bruno Berselli, Feb 06 2015
Primes:= select(isprime, [2,$3..100]): seq(ilcm($2..Primes[i]-1),i=1..nops(Primes)); # Robert Israel, Jul 19 2016
LCM@@Range[#]&/@(Prime[Range[20]]-1) (* Harvey P. Dale, Jan 30 2015 *)
/* By definition (slow): */
S:=[]; for n in [1..9] do k:=1; while not forall{j: j in [2..NthPrime(n)-1] | IsOne(k*NthPrime(n) mod j)} do k:=k+1; end while; Append(~S, k); end for; S; /* or */
[p eq 2 select 1 else Modinv(p, Lcm([1..p-1])): p in PrimesUpTo(60)];// Bruno Berselli, Feb 08 2015
a[1] = a[2] = 1; a[n_] := Module[{p, m, r, r0, r1}, p = Prime[n]; m = LCM @@ Range[2, p-1]; r = Reduce[k>0 && p*k + m*j == 1, {k, j}, Integers]; r0 = r /. C[] -> 0; r1 = r /. C[] -> 1 ; If[r0 === False, r1[[1, 2]], Min[r0[[1, 2]], r1[[1, 2]]]]]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Feb 09 2015 *)
Prime(4) = 7, a(4) = 119 = 7*17 because 119 is smallest multiple of 7 such that 119 mod 1 = 0, 119 mod 2 = 1, 119 mod 3 = 2, 119 mod 4 = 3, 119 mod 5 = 4, 119 mod 6 = 5.
for(n=1, 10, p=prime(n); forstep(m=p, 10^11, p, forstep(j=p-1, 1, -1, if(m%j<>j-1, next(2))); print(n " " m); next(2))) \\ Donovan Johnson, Dec 30 2013
Comments