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A111656 n-th prime appears n-th composite number times. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6: 64-94 (1962).

L. Panaitopol, Some Properties of the Series of Composed [Composite] Numbers, J. Inequalities in Pure and Applied Mathematics. 2(2): Article 38, 2000.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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Last modified January 18 16:43 EST 2022. Contains 350455 sequences. (Running on oeis4.)