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A050519 Increments of arithmetic progression of at least 6 terms having the same value of phi in A050518.

%I A050519 #43 Jun 25 2017 00:00:35
%S A050519 30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,540,
%T A050519 570,600,630,660,690,720,750,780,810,840,870,900,930,960,990,1020,
%U A050519 1050,1080,1110,1140,1170,1200,1230,1260,1290,1320,1350,1380,1410,1440,1470
%N A050519 Increments of arithmetic progression of at least 6 terms having the same value of phi in A050518.
%C A050519 The first 112 terms are successive multiples of 30, but this sequence does not coincide with A249674: a(113) = 210. See the Khovanova link and comments in A050518.
%C A050519 The increments <= 1000 for terms of A050518 between 13413600 and 10^9 (see comment on A050518) are 720, 750, 780, 810, 840, 870, 900, 930, 960, 990, 210, 210, 420, 30, 420, 630, 630, 840, 60, 840, 90, 30, 30, 120, 150, 30, 18. - _Mauro Fiorentini_, Apr 12 2015
%H A050519 Robert Israel, <a href="/A050519/b050519.txt">Table of n, a(n) for n = 1..114</a>
%H A050519 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a>
%p A050519 N:= 10^7: # to get all terms <= N in A050518
%p A050519 with(numtheory):
%p A050519 Res:= NULL:
%p A050519 phis:= {seq(phi(i), i=2..N)}:
%p A050519 for m in phis do
%p A050519    S:= convert(invphi(m), set);
%p A050519    if nops(S) < 6 then next fi;
%p A050519    for d from 0 to 4 do
%p A050519      Sd[d]:= select(t-> (t mod 5 = d), S, d);
%p A050519      nd:= nops(Sd[d]);
%p A050519      for i0 from 1 to nd-1 do
%p A050519        s0:= Sd[d][i0];
%p A050519        if s0 > N then break fi;
%p A050519        for i5 from i0+1 to nd do
%p A050519          s5:= Sd[d][i5];
%p A050519          incr:= (s5 - s0)/5;
%p A050519          if {s0+incr, s0+2*incr, s0+3*incr, s0+4*incr} subset S then
%p A050519            Res:= Res, [s0, incr];
%p A050519          fi
%p A050519        od
%p A050519      od;
%p A050519    od;
%p A050519 od:
%p A050519 sort([Res], (s, t)->s[1]<t[1]); # gives both A050518 and A050519 entries map2(op, 2, %); # _Robert Israel_, Apr 30 2015
%Y A050519 Cf. A000010, A050495, A050496, A050497, A050515-A050520.
%K A050519 nonn
%O A050519 1,1
%A A050519 _Jud McCranie_, Dec 28 1999
%E A050519 More terms from _Mauro Fiorentini_, Apr 12 2015