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A055396 Smallest prime dividing n is a(n)-th prime (a(1)=0). 41
0, 1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 1, 6, 1, 2, 1, 7, 1, 8, 1, 2, 1, 9, 1, 3, 1, 2, 1, 10, 1, 11, 1, 2, 1, 3, 1, 12, 1, 2, 1, 13, 1, 14, 1, 2, 1, 15, 1, 4, 1, 2, 1, 16, 1, 3, 1, 2, 1, 17, 1, 18, 1, 2, 1, 3, 1, 19, 1, 2, 1, 20, 1, 21, 1, 2, 1, 4, 1, 22, 1, 2, 1, 23, 1, 3, 1, 2, 1, 24, 1, 4, 1, 2, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A000040(a(n)) = A020639(n); a(n) <= A061395(n). - Reinhard Zumkeller, May 22 2003

Grundy numbers of the game in which you decrease n by a number prime to n, and the game ends when 1 is reached. - Eric M. Schmidt, Jul 21 2013

REFERENCES

John H. Conway, On Numbers and Games, 2nd Edition, p. 129.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences generated by sieves

FORMULA

a(n) = A049084(A020639(n)). - Reinhard Zumkeller, May 22 2003

EXAMPLE

a(15) = 2 because 15=3*5, 3<5 and 3 is the 2nd prime.

MAPLE

with(numtheory):

a:= n-> `if`(n=1, 0, pi(min(factorset(n)[]))):

seq(a(n), n=1..100);  # Alois P. Heinz, Aug 03 2013

MATHEMATICA

a[1] = 0; a[n_] := PrimePi[ FactorInteger[n][[1, 1]] ]; Table[a[n], {n, 1, 96}](* Jean-Fran├žois Alcover, Jun 11 2012 *)

PROG

(Haskell)

a055396 = a049084 . a020639  -- Reinhard Zumkeller, Apr 05 2012

CROSSREFS

Cf. sieve of Eratosthenes: A004280, A038179, A055399.

Sequence in context: A087267 A128267 A028920 * A057499 A241919 A064839

Adjacent sequences:  A055393 A055394 A055395 * A055397 A055398 A055399

KEYWORD

nonn

AUTHOR

Henry Bottomley, May 15 2000

STATUS

approved

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Last modified November 22 11:41 EST 2014. Contains 249805 sequences.