A180096 a(n) is the smallest number k such that four consecutive prime numbers prime(n), prime(n+1), prime(n+2) and prime(n+3) are divisors of k, k+1, k+2 and k+3 respectively.

158, 789, 790, 6797, 4367, 33761, 63478, 50806, 464347, 164981, 1763900, 459281, 707865, 1886109, 7764870, 5475907, 17050292, 20242240, 7046323, 28747545, 1463869, 27141082, 55086104, 48982574, 70173486, 18969921, 81436950, 23448515, 148589236, 233188382

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 100 terms from Alois P. Heinz)

Example

a(1) = 158 is a term because prime(1) = 2 =>
  158 = 2*79; 159 = 3*53; 160 = 5*32; 161 = 7*23.
a(14) = 1886109 is a term because prime(14) = 43 =>
  1886109 = 43*43863; 1886110 = 47*40130; 1886111 = 53*35587; 1886112 = 59*31968.

Maple

A180096 := proc(n) p := ithprime(n) ; q := nextprime(p) ; r := nextprime(q) ; s := nextprime(r) ; for k from p by p do if modp(k+1, q)=0 and modp(k+2, r) =0 and modp(k+3, s) = 0 then return k; end if; end do: end proc: # R. J. Mathar, Sep 13 2011

Mathematica

a[n_] := a[n] = Module[{p = Prime[n], q, r, s}, q = NextPrime[p]; r = NextPrime[q]; s = NextPrime[r]; For[k = p, True, k += p, If[Mod[k+1, q] == 0 && Mod[k+2, r] == 0 && Mod[k+3, s] == 0, Return[k]]]];
Table[Print[a[n]]; a[n], {n, 1, 30}] (* Jean-François Alcover, May 17 2020, after Maple *)

Prog

(Sage) def A180096(n): return crt([-3..0][::-1], [nth_prime(i) for i in [n..n+3]]) # D. S. McNeil, Jan 16 2011
(PARI) a(n) = my(p=prime(n), v=concat(p, vector(3, i, p=nextprime(p+1)))); m=vector(4, i, Mod(-i+1, v[i])); sol=m[1]; for(i=2, 4, sol = chinese(sol, m[i])); lift(sol) \\ David A. Corneth, Apr 13 2019

Crossrefs

Cf. A077338, A180095.

Sequence in context: A380474 A189813 A270791 * A250996 A280483 A252359

Adjacent sequences: A180093 A180094 A180095 * A180097 A180098 A180099

Keyword

nonn

Author

Michel Lagneau, Jan 16 2011

Status

approved