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

1,1

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

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]<t[1]); # gives both A050518 and A050519 entries map2(op, 2, %); # Robert Israel, Apr 30 2015

Crossrefs

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

Sequence in context: A246947 A226944 A249674 * A358756 A069819 A143207

Adjacent sequences: A050516 A050517 A050518 * A050520 A050521 A050522

Keyword

nonn

Author

Jud McCranie, Dec 28 1999

Extensions

More terms from Mauro Fiorentini, Apr 12 2015

Status

approved