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 A111656 #16 Feb 16 2025 08:32:58
%S A111656 2,2,2,2,3,3,3,3,3,3,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,11,11,11,11,11,
%T A111656 11,11,11,11,11,13,13,13,13,13,13,13,13,13,13,13,13,17,17,17,17,17,17,
%U A111656 17,17,17,17,17,17,17,17,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19
%N A111656 n-th prime appears n-th composite number times.
%D A111656 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 2.
%H A111656 Harvey P. Dale, <a href="/A111656/b111656.txt">Table of n, a(n) for n = 1..1000</a>
%H A111656 L. Panaitopol, <a href="http://emis.icm.edu.pl/journals/JIPAM/v2n3/027_01.html">Some Properties of the Series of Composed Numbers</a>, J. Inequalities in Pure and Applied Mathematics. 2(2): Article 38, 2000.
%H A111656 J. B. Rosser and L. Schoenfeld, <a href="https://doi.org/10.1215/ijm/1255631807">Approximate formulas for some functions of prime numbers</a>, Illinois J. Math. 6: 64-94 (1962).
%H A111656 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompositeNumber.html">Composite Number</a>.
%H A111656 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeNumber.html">Prime Number</a>.
%F A111656 A000040(n) appears A002808(n) times.
%t A111656 Module[{nn=20,cm,pr,len},cm=Select[Range[nn],CompositeQ];len = Length[ cm];Table[#[[1]],#[[2]]]&/@Thread[{Prime[Range[len]],cm}]]//Flatten (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 06 2018 *)
%Y A111656 Cf. A000040, A002808, A111653, A111654, A111655, A111657.
%K A111656 easy,nonn
%O A111656 1,1
%A A111656 _Jonathan Vos Post_, Aug 12 2005