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A199547
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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).
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13
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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
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OFFSET
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1,1
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COMMENTS
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J. E. Littlewood (1914) proved that this sequence is infinite.
a(1) = 26861 was found in 1957 by John Leech.
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REFERENCES
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Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, p. 22.
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LINKS
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FORMULA
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MATHEMATICA
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lst = {}; For[n = 2; t = 0, n < 50451, n++, t += Mod[p = Prime[n], 4] - 2; If[t < 0, AppendTo[lst, p]]]; lst
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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