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).

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

Prog

(Python)
from sympy import nextprime; a, p = 0, 2
while p < 617717:
    p=nextprime(p); a += p%4-2
    if a < 0: print(p, end = ', ') # Ya-Ping Lu, Jan 18 2025

Crossrefs

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

Sequence in context: A093181 A235751 A235814 * A051025 A048921 A269115

Adjacent sequences: A199544 A199545 A199546 * A199548 A199549 A199550

Keyword

nonn,changed

Author

Arkadiusz Wesolowski, Dec 09 2011

Status

approved