A243390 Numbers k such that, taken pairwise, k, prime(k) and phi(k) have no common digits.

2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 20, 22, 39, 44, 46, 48, 65, 66, 77, 87, 93, 99, 123, 134, 146, 154, 165, 230, 246, 430, 441, 446, 494, 522, 528, 552, 555, 566, 622, 662, 711, 737, 738, 740, 825, 855, 984, 1155, 1160, 1170, 1180, 1214, 2230, 5055, 8878

Offset

1,1

Comments

a(95) > 10^10 if it exists. - David A. Corneth, Aug 25 2020

Links

David A. Corneth, Table of n, a(n) for n = 1..94

Example

n = 1214, prime(1214) = 9839, phi(1214) = 606; (1214,9839), (1214,606) and (9839,606) have no common digits. So 1214 is in the sequence.

Mathematica

ncdQ[n_]:=Module[{a=IntegerDigits[n], b=IntegerDigits[Prime[n]], c = IntegerDigits[ EulerPhi[n]]}, Intersection[a, b] == Intersection[b, c] == Intersection[a, c]=={}]; Select[Range[9000], ncdQ] (* Harvey P. Dale, Aug 24 2020 *)

Prog

(PARI)
{ s=[];
  for(n=1, 50000,
    u=vecsort(digits(n), , 8);
    v=vecsort(digits(prime(n)), , 8);
    w=vecsort(digits(eulerphi(n)), , 8);
    if(setintersect(u, v)==[]&&setintersect(u, w)==[]&&setintersect(v, w)==[],
      s=concat(s, n)
    )
  );
  s }
(PARI) upto(n) = {my(t=1, res=List()); forprime(p=2, oo, st=Set(digits(t)); sp=Set(digits(p)); if(#setintersect(st, sp)==0, se=Set(digits(eulerphi(t))); if(#setintersect(st, se)==0 && #setintersect(sp, se)==0, listput(res, t))); t++; if(t>=n, return(res)))} \\ David A. Corneth, Aug 25 2020

Crossrefs

Cf. A000010, A000040, A243355, A243356.

Sequence in context: A291719 A360425 A018609 * A029461 A128168 A232823

Adjacent sequences: A243387 A243388 A243389 * A243391 A243392 A243393

Keyword

nonn,base

Author

Colin Barker, Jun 04 2014

Status

approved