login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Positions of zeros in A270434; numbers n for which A270432(n) = A270433(n).
2

%I #12 Nov 25 2021 08:54:59

%S 96,220,222,226,272,274,276,288,376,380,394,396,398,412,414,416,422,

%T 434,448,458,462,464,466,472,476,480,482,484,486,506,508,512,514,522,

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

%C 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 No other terms after a(2651) = 2346398 in range 1 .. 2^25.

%H Antti Karttunen, <a href="/A270435/b270435.txt">Table of n, a(n) for n = 1..2651</a>

%t 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 (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A270435 (ZERO-POS 1 1 A270434))

%Y Cf. A048673, A064216, A270432, A270433, A270434.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 17 2016