This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A205558 (A204898)/2 = (prime(k)-prime(j))/2; A086802 without its zeros. 58
 1, 2, 1, 4, 3, 2, 5, 4, 3, 1, 7, 6, 5, 3, 2, 8, 7, 6, 4, 3, 1, 10, 9, 8, 6, 5, 3, 2, 13, 12, 11, 9, 8, 6, 5, 3, 14, 13, 12, 10, 9, 7, 6, 4, 1, 17, 16, 15, 13, 12, 10, 9, 7, 4, 3, 19, 18, 17, 15, 14, 12, 11, 9, 6, 5, 2, 20, 19, 18, 16, 15, 13, 12, 10, 7, 6, 3, 1, 22, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let p(n) denote the n-th prime.  If c is a positive integer, there are infinitely many pairs (k,j) such that c divides p(k)-p(j).  The set of differences p(k)-p(j) is ordered as a sequence at A204890.  Guide to related sequences: c....k..........j..........p(k)-p(j).[p(k)-p(j)]/c 2....A133196....A131818....A204898....A205558 3....A205560....A205547....A205557....A205675 4....A205677....A205678....A205681....A205682 5....A205684....A205685....A205688....A205689 6....A205691....A205692....A205695....A205696 7....A205698....A205699....A205702....A205703 8....A205705....A205706....A205709....A205710 9....A205712....A205713....A205716....A205717 10...A205720....A205721....A205724....A205725 LINKS EXAMPLE Writing prime(k) as p(k), p(3)-p(2)=5-3=2 p(4)-p(2)=7-3=4 p(4)-p(3)=7-5=2 p(5)-p(2)=11-3=8 p(5)-p(3)=11-5=6 p(5)-p(4)=11-7=4, so that the first 6 terms of A205558 are 1,2,1,4,3,2. The sequence can be regarded as a rectangular array in which row n is given by [prime(n+2+k)-prime(n+1)]/2; a northwest corner follows: 1...2...4...5...7...8....10...13...14...17...19...20 1...3...4...6...7...9....12...13...16...18...19...21 2...3...5...6...8...11...12...15...17...18...20...23 1...3...4...6...9...10...13...15...16...18...21...24 2...3...5...8...9...12...14...15...17...20...23...24 1...3...6...7...10..12...13...15...18...21...22...25 2...5...6...9...11..12...14...17...20...21...24...26 - Clark Kimberling, Sep 29 2013 MATHEMATICA s[n_] := s[n] = Prime[n]; z1 = 200; z2 = 80; f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2]; Table[s[n], {n, 1, 30}]              (* A000040 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}]              (* A204890 *) 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] = Delete[w[n], Position[w[n], 0]] c = 2; t = d[c]                      (* A080036 *) k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2] j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2 Table[k[n], {n, 1, z2}]                  (* A133196 *) Table[j[n], {n, 1, z2}]                  (* A131818 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204898 *) Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205558 *) CROSSREFS Cf. A205675, A205560, A204892. Sequence in context: A087850 A087849 A075015 * A082494 A194187 A174375 Adjacent sequences:  A205555 A205556 A205557 * A205559 A205560 A205561 KEYWORD nonn AUTHOR Clark Kimberling, Jan 30 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 20 14:06 EDT 2019. Contains 326152 sequences. (Running on oeis4.)