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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).

%I A199547 #39 Jan 18 2025 16:04:24
%S A199547 26861,616841,616849,616877,616897,616909,616933,616943,616951,616961,
%T A199547 616991,616997,616999,617011,617269,617273,617293,617311,617327,
%U A199547 617333,617339,617341,617359,617369,617401,617429,617453,617521,617537,617689,617693,617699,617717
%N 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).
%C A199547 Another version of A007350.
%C A199547 J. E. Littlewood (1914) proved that this sequence is infinite.
%C A199547 a(1) = 26861 was found in 1957 by John Leech.
%C A199547 Prime indices of negative terms in A066520. - _Jianing Song_, Feb 20 2019
%D A199547 Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, p. 22.
%H A199547 Arkadiusz Wesolowski, <a href="/A199547/b199547.txt">Table of n, a(n) for n = 1..1000</a>
%H A199547 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/17.html">Prime Curios! 26861</a>
%F A199547 a(n) = prime(A096628(n)). - _Jianing Song_, Feb 20 2019
%t A199547 lst = {}; For[n = 2; t = 0, n < 50451, n++, t += Mod[p = Prime[n], 4] - 2; If[t < 0, AppendTo[lst, p]]]; lst
%o A199547 (Python)
%o A199547 from sympy import nextprime; a, p = 0, 2
%o A199547 while p < 617717:
%o A199547     p=nextprime(p); a += p%4-2
%o A199547     if a < 0: print(p, end = ', ') # _Ya-Ping Lu_, Jan 18 2025
%Y A199547 Cf. A007350, A038691, A038698, A051024, A051025, A066520, A096628.
%K A199547 nonn
%O A199547 1,1
%A A199547 _Arkadiusz Wesolowski_, Dec 09 2011