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.

A270435 Positions of zeros in A270434; numbers n for which A270432(n) = A270433(n).

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%I A270435 #12 Nov 25 2021 08:54:59
%S A270435 96,220,222,226,272,274,276,288,376,380,394,396,398,412,414,416,422,
%T A270435 434,448,458,462,464,466,472,476,480,482,484,486,506,508,512,514,522,
%U A270435 524,528,590,592,594,596,618,620,622,636,638,648,652,654,656,658,662,678,680,682,684,686,688,704,706,708,992,1008,1016,1024
%N A270435 Positions of zeros in A270434; numbers n for which A270432(n) = A270433(n).
%C A270435 Numbers n for which in the range 1 .. n there are exactly the same number of s's such that A048673(s) and A064216(s) are of the same parity than there are t's such that A048673(t) and A064216(t) are of opposite parity.
%C A270435 No other terms after a(2651) = 2346398 in range 1 .. 2^25.
%H A270435 Antti Karttunen, <a href="/A270435/b270435.txt">Table of n, a(n) for n = 1..2651</a>
%t A270435 nn = 2048; f[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; g[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; s = Select[Range@ nn, Xor[EvenQ@ f@ #, OddQ@ g@ #] &]; t = Select[Range@ nn, Xor[EvenQ@ f@ #, EvenQ@ g@ #] &]; Flatten@ Position[Table[Count[s, k_ /; k <= n] - Count[t, k_ /; k <= n], {n, nn/2}], n_ /; n == 0] (* _Michael De Vlieger_, Mar 19 2016 *)
%o A270435 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A270435 (define A270435 (ZERO-POS 1 1 A270434))
%Y A270435 Cf. A048673, A064216, A270432, A270433, A270434.
%K A270435 nonn
%O A270435 1,1
%A A270435 _Antti Karttunen_, Mar 17 2016