A204908 Least k such that n divides s(k)-s(j) for some j in [1,k], where s(k) is the k-th prime >=5.
2, 2, 3, 3, 5, 3, 6, 4, 7, 5, 8, 5, 9, 6, 10, 7, 11, 7, 12, 9, 13, 8, 14, 8, 16, 9, 15, 11, 18, 10, 17, 10, 18, 11, 21, 11, 20, 12, 21, 13, 22, 13, 23, 16, 23, 14, 24, 14, 25, 16
Offset: 1
Keywords
Links
- Jinyuan Wang, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
s[n_] := s[n] = Prime[n + 2]; z1 = 400; z2 = 50; Table[s[n], {n, 1, 30}] (* primes >=5 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}] (* A204906 *) v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0] w[n_] := w[n] = Table[v[n, h], {h, 1, z1}] d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]] Table[d[n], {n, 1, z2}] (* A204907 *) k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2] m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2] j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2 Table[k[n], {n, 1, z2}] (* A204908 *) Table[j[n], {n, 1, z2}] (* A204909 *) Table[s[k[n]], {n, 1, z2}] (* A204910 *) Table[s[j[n]], {n, 1, z2}] (* A204911 *) -
PARI
a(n) = {my(p=5, k=1); while(sum(i=5, p-1, isprime(i)&&(p-i)%n==0)==0, p=nextprime(p+1); k++); k; } \\ Jinyuan Wang, Jan 30 2020
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