This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A190895 #27 Aug 11 2023 10:02:45 %S A190895 1,5,6,11,12,23,24,47,48,50,51,101,102,105,110,111,117,233,234,467, %T A190895 468,470,471,941,942,945,1889,1890,3779,3780,7559,7560,7566,15131, %U A190895 15132,15158,15159,15162,30323,30324,60647,60648,60650,60651,60701,60702,121403,121404,242807,242808,242810 %N A190895 Auxiliary r(n) sequence used to prove some properties about Rowland's sequence: r(1) = 1, and r(n) = 1/2*(c(n)+1), where c(n) is A190894, for n>1. %C A190895 This sequence is matched with another auxiliary sequence called c(n) (A190894). Rowland's sequence (A106108) can be easily described in terms of c(n) and r(n). Also, they can be used to prove easily that the difference between two consecutive terms is always 1 or a prime. %C A190895 This sequence is related to Rowland's sequence (A106108) with initial condition a(1)=7. %C A190895 Sequence r(n) satisfies 2r(n) - 1 = c(n), for any n>1. %C A190895 For further information, see the references. %H A190895 F. Chamizo, D. Raboso, and S. Ruiz-Cabello, <a href="https://doi.org/10.37236/2006">On Rowland's sequence</a>, Electronic J. Combin., Vol. 18(2), 2011, #P10. %H A190895 E. S. Rowland, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Rowland/rowland21.html">A natural prime-generating recurrence</a>, J. Integer Seq., 11(2): Article 08.2.8, 13, 2008. %e A190895 For n = 2, r(2) = 1/2 * (c(2) + 1) = 1/2 * (9 + 1) = 5. %e A190895 For n = 3, r(3) = 1/2 * (c(3) + 1) = 1/2 * (11 + 1) = 6. %Y A190895 Cf. A106108, A190894. %K A190895 nonn %O A190895 1,2 %A A190895 _Serafín Ruiz-Cabello_, May 23 2011