

A038691


Indices of primes at which the prime race 4k1 vs. 4k+1 is tied.


23



1, 3, 7, 13, 89, 2943, 2945, 2947, 2949, 2951, 2953, 50371, 50375, 50377, 50379, 50381, 50393, 50413, 50423, 50425, 50427, 50429, 50431, 50433, 50435, 50437, 50439, 50445, 50449, 50451, 50503, 50507, 50515, 50517, 50821, 50843, 50853
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OFFSET

1,2


COMMENTS

Starting from a(27410) = 316064952537 the sequence includes the 8th signchanging zone predicted by C. Bays et al back in 2001. The sequence with the first 8 signchanging zones contains 419467 terms (see afile) with a(419467) = 330797040309 as its last term.  Sergei D. Shchebetov, Oct 16 2017


REFERENCES

Stan Wagon, The Power of Visualization, Front Range Press, 1994, pp. 23.


LINKS

A. Granville and G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 133.
M. Rubinstein and P. Sarnak, Chebyshev’s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173197.


EXAMPLE

a(n) is the nth number m at which the prime race 4k1 vs. 4k+1 is tied:
.
count

m p=prime(m) p mod 4 4k1 4k+1
    
1 2 2 0 = 0 a(1)=1
2 3 1 1 0
3 5 +1 1 = 1 a(2)=3
4 7 1 2 1
5 11 1 3 1
6 13 +1 3 2
7 17 +1 3 = 3 a(3)=7
8 19 1 4 3
9 23 1 5 3
10 29 +1 5 4
11 31 1 6 4
12 37 +1 6 5
13 41 +1 6 = 6 a(4)=13
(End)


MATHEMATICA

Flatten[ Position[ FoldList[ Plus, 0, Mod[ Prime[ Range[ 2, 50900 ] ], 4 ]2 ], 0 ] ]


PROG

(PARI) lista(nn) = {nbp = 0; nbm = 0; forprime(p=2, nn, if (((p1) % 4) == 0, nbp++, if (((p+1) % 4) == 0, nbm++)); if (nbm == nbp, print1(primepi(p), ", ")); ); } \\ Michel Marcus, Nov 20 2016


CROSSREFS

Cf. A002145, A002313, A007350, A007351, A038698, A051024, A051025, A066520, A096628, A096447, A096448, A199547


KEYWORD

nonn


AUTHOR



STATUS

approved



