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A180096
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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.
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3
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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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]]]];
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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