

A096449


Primes p such that the number of primes q, 5 <= q < p, congruent to 1 mod 3, is equal to the number of such primes congruent to 2 mod 3.


4



5, 11, 17, 23, 41, 47, 83, 167, 227, 233, 608981812919, 608981812961, 608981813017, 608981813569, 608981813677, 608981813833, 608981813851, 608981813927, 608981813939, 608981813963, 608981814043, 608981814149, 608981814251, 608981814827
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OFFSET

1,1


COMMENTS

First term prime(3) = 5 is placed on 0th row.
If prime(n1) = +1 mod 3 is on kth row then we put prime(n) on (k1)st row.
If prime(n1) = 1 mod 3 is on kth row then we put prime(n) on (k+1)st row.
This process makes an array of prime numbers:
5, 11, 17, 23, 41, 47, 83, ... (this sequence)
7, 13, 19, 29, 37, 43, 53, 71, 79, 89, 101, .. (A096452).
31, 59, 67, 73, 97, ... (A096453)
61, ...


LINKS

Table of n, a(n) for n=1..24.


FORMULA

For n>1, a(n) = prime(A096629(n1)+1) = A000040(A096629(n1)+1).  Max Alekseyev, Sep 19 2009
a(n) = A151800(A098044(n)) = A007918(A098044(n)+1).


MATHEMATICA

lst = {5}; p = 0; q = 0; r = 5; While[r < 10^9, If[ Mod[r, 3] == 2, p++, q++ ]; r = NextPrime@r; If[p == q, AppendTo[lst, r]; Print@r]]; lst (* Robert G. Wilson v, Sep 20 2009 *)


CROSSREFS

Cf. A096448A096455.
Sequence in context: A096448 A147305 A049755 * A268640 A214912 A216551
Adjacent sequences: A096446 A096447 A096448 * A096450 A096451 A096452


KEYWORD

nonn


AUTHOR

Yasutoshi Kohmoto, Aug 12 2004


EXTENSIONS

More terms and better definition from Joshua Zucker, May 21 2006
Terms a(11) onward from Max Alekseyev, Feb 10 2011


STATUS

approved



