

A112632


Excess of 3k1 primes over 3k+1 primes, beginning with 2.


5



1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 2, 1, 2, 3, 4, 3, 4, 3, 4, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 5, 6, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 3, 4, 3, 4, 5, 4, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 5
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OFFSET

1,3


COMMENTS

Cumulative sums of A134323. The first negative term is a(23338590792) for the prime 608981813029. See page 4 of the paper by Granville and Martin.  T. D. Noe, Jan 23 2008


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000
A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 133.


EXAMPLE

a(1)=1 because 2 is 1 mod 3
a(2)=1 because 3 is 0 mod 3 and does not change the accounting
a(3)=2 because 5 is 1 mod 3
a(4)=1 because 7 is 1 mod 3


MATHEMATICA

a[n_] := a[n] = a[n1] + If[Mod[Prime[n], 6] == 1, 1, 1]; a[1] = a[2] = 1; Table[a[n], {n, 1, 100}] (* JeanFrançois Alcover, Jul 24 2012 *)
Accumulate[Which[IntegerQ[(#+1)/3], 1, IntegerQ[(#1)/3], 1, True, 0]& /@ Prime[ Range[100]]] (* Harvey P. Dale, Jun 06 2013 *)


PROG

(Haskell)
a112632 n = a112632_list !! (n1)
a112632_list = scanl1 (+) $ map negate a134323_list
 Reinhard Zumkeller, Sep 16 2014


CROSSREFS

Cf. A038698, A007352, A098044.
Cf. A134323.
Sequence in context: A103682 A023134 A272863 * A254575 A275344 A206826
Adjacent sequences: A112629 A112630 A112631 * A112633 A112634 A112635


KEYWORD

sign,nice


AUTHOR

Roger Hui, Dec 22 2005


STATUS

approved



