A111656 n-th prime appears n-th composite number times.

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, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19

Offset: 1

Author

Jonathan Vos Post, Aug 12 2005

Keywords

• easy
• nonn

References

• T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 2.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• L. Panaitopol, Some Properties of the Series of Composed Numbers, J. Inequalities in Pure and Applied Mathematics. 2(2): Article 38, 2000.
• J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6: 64-94 (1962).
• Eric Weisstein's World of Mathematics, Composite Number.
• Eric Weisstein's World of Mathematics, Prime Number.

Crossrefs

Cf. A000040, A002808, A111653, A111654, A111655, A111657.

Programs

Mathematica

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 *)

Formula

A000040(n) appears A002808(n) times.