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

30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 870, 900, 930, 960, 990, 1020, 1050, 1080, 1110, 1140, 1170, 1200, 1230, 1260, 1290, 1320, 1350, 1380, 1410, 1440, 1470

Offset: 1

Author

Jud McCranie, Dec 28 1999

Keywords

• nonn

Comments

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.

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

Links

• Robert Israel, Table of n, a(n) for n = 1..114
• Tanya Khovanova, Non Recursions

Crossrefs

Cf. A000010, A050495, A050496, A050497, A050515-A050520.

Programs

Maple

N:= 10^7: # to get all terms <= N in A050518
with(numtheory):
Res:= NULL:
phis:= {seq(phi(i), i=2..N)}:
for m in phis do
   S:= convert(invphi(m), set);
   if nops(S) < 6 then next fi;
   for d from 0 to 4 do
     Sd[d]:= select(t-> (t mod 5 = d), S, d);
     nd:= nops(Sd[d]);
     for i0 from 1 to nd-1 do
       s0:= Sd[d][i0];
       if s0 > N then break fi;
       for i5 from i0+1 to nd do
         s5:= Sd[d][i5];
         incr:= (s5 - s0)/5;
         if {s0+incr, s0+2*incr, s0+3*incr, s0+4*incr} subset S then
           Res:= Res, [s0, incr];
         fi
       od
     od;
   od;
od:
sort([Res], (s, t)->s[1]A050518 and A050519 entries map2(op, 2, %); # Robert Israel, Apr 30 2015

Extensions

More terms from Mauro Fiorentini, Apr 12 2015