cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A330359 Race of lucky numbers of the form 4*k - 1 vs. 4*k + 1 is tied at the a(n)-th lucky number.

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%I A330359 #9 Dec 13 2019 02:57:31
%S A330359 2,4,6,16,20,22,24,2684,2686,2688,2696,2710,2712,109978,110026,110028,
%T A330359 110030,110052,110056,110060,110068,110070,110154,110156,110158,
%U A330359 110160,118048,118050,118126,118128,118130,118132,118134,118136,118138,118152,118154,118156
%N A330359 Race of lucky numbers of the form 4*k - 1 vs. 4*k + 1 is tied at the a(n)-th lucky number.
%C A330359 All the terms are even by definition. For each term m, there are m/2 lucky numbers of the form 4*k - 1 and m/2 lucky numbers of the form 4*k + 1 up to the m-th lucky number.
%C A330359 Gardiner et al. (1956) noted that the ratio between the numbers of lucky numbers of the form 4*k - 1 and 4*k + 1 seems to tend to 1, with a preponderance, at first, of the lucky numbers of the form 4*k + 3.
%H A330359 Vema Gardiner, Roger Lazarus, Nicholas Metropolis and Stanislaw Ulam, <a href="https://doi.org/10.2307/3029719">On certain sequences of integers defined by sieves</a>, Mathematics Magazine, Vol. 29, No. 3 (1956), pp. 117-122. See Table IV, p. 121.
%e A330359 6 is in the sequence since the first 6 lucky numbers are 1, 3, 7, 9, 13, 15, half of them are of the form 4*k-1 (3, 7, 15) and half of the form 4*k+1 (1, 9, 13).
%t A330359 lucky = Import["b000959.txt", "Table"][[;; , 2]]; Flatten[Position[Accumulate[ Mod[lucky, 4] - 2], 0]] (* use the b-file from A000959 *)
%Y A330359 Cf. A000959, A038691, A137168, A137170, A330360, A330361.
%K A330359 nonn
%O A330359 1,1
%A A330359 _Amiram Eldar_, Dec 12 2019