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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. 3

%I

%S 158,789,790,6797,4367,33761,63478,50806,464347,164981,1763900,459281,

%T 707865,1886109,7764870,5475907,17050292,20242240,7046323,28747545,

%U 1463869,27141082,55086104,48982574,70173486,18969921,81436950,23448515,148589236,233188382

%N 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.

%H David A. Corneth, <a href="/A180096/b180096.txt">Table of n, a(n) for n = 1..10000</a> (first 100 terms from Alois P. Heinz)

%e a(1) = 158 is a term because prime(1) = 2 =>

%e 158 = 2*79; 159 = 3*53; 160 = 5*32; 161 = 7*23.

%e a(14) = 1886109 is a term because prime(14) = 43 =>

%e 1886109 = 43*43863; 1886110 = 47*40130; 1886111 = 53*35587; 1886112 = 59*31968.

%p 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

%t 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]]]];

%t Table[Print[a[n]]; a[n], {n, 1, 30}] (* _Jean-Fran├žois Alcover_, May 17 2020, after Maple *)

%o (Sage) def A180096(n): return crt([-3..0][::-1], [nth_prime(i) for i in [n..n+3]]) # _D. S. McNeil_, Jan 16 2011

%o (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

%Y Cf. A077338, A180095.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jan 16 2011

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Last modified May 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)