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

1,1

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.

Formula

A000040(n) appears A002808(n) times.

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 *)

Crossrefs

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

Sequence in context: A076471 A339391 A165116 * A165118 A342882 A025423

Adjacent sequences: A111653 A111654 A111655 * A111657 A111658 A111659

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 12 2005

Status

approved