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A199547
Primes p for which pi_{4,3}(p) < pi_{4,1}(p), where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).
13
26861, 616841, 616849, 616877, 616897, 616909, 616933, 616943, 616951, 616961, 616991, 616997, 616999, 617011, 617269, 617273, 617293, 617311, 617327, 617333, 617339, 617341, 617359, 617369, 617401, 617429, 617453, 617521, 617537, 617689, 617693, 617699, 617717
OFFSET
1,1
COMMENTS
Another version of A007350.
J. E. Littlewood (1914) proved that this sequence is infinite.
a(1) = 26861 was found in 1957 by John Leech.
Prime indices of negative terms in A066520. - Jianing Song, Feb 20 2019
REFERENCES
Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, p. 22.
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 26861
FORMULA
a(n) = prime(A096628(n)). - Jianing Song, Feb 20 2019
MATHEMATICA
lst = {}; For[n = 2; t = 0, n < 50451, n++, t += Mod[p = Prime[n], 4] - 2; If[t < 0, AppendTo[lst, p]]]; lst
KEYWORD
nonn
AUTHOR
STATUS
approved