A199547 - OEIS

%I #39 Jan 18 2025 16:04:24

%S 26861,616841,616849,616877,616897,616909,616933,616943,616951,616961,

%T 616991,616997,616999,617011,617269,617273,617293,617311,617327,

%U 617333,617339,617341,617359,617369,617401,617429,617453,617521,617537,617689,617693,617699,617717

%N 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 Another version of A007350.

%C J. E. Littlewood (1914) proved that this sequence is infinite.

%C a(1) = 26861 was found in 1957 by John Leech.

%C Prime indices of negative terms in A066520. - _Jianing Song_, Feb 20 2019

%D Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, p. 22.

%H Arkadiusz Wesolowski, <a href="/A199547/b199547.txt">Table of n, a(n) for n = 1..1000</a>

%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/17.html">Prime Curios! 26861</a>

%F a(n) = prime(A096628(n)). - _Jianing Song_, Feb 20 2019

%t lst = {}; For[n = 2; t = 0, n < 50451, n++, t += Mod[p = Prime[n], 4] - 2; If[t < 0, AppendTo[lst, p]]]; lst

%o (Python)

%o from sympy import nextprime; a, p = 0, 2

%o while p < 617717:

%o     p=nextprime(p); a += p%4-2

%o     if a < 0: print(p, end = ', ') # _Ya-Ping Lu_, Jan 18 2025

%Y Cf. A007350, A038691, A038698, A051024, A051025, A066520, A096628.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Dec 09 2011