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A243390 Numbers k such that, taken pairwise, k, prime(k) and phi(k) have no common digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A035303 A291719 A018609 * A029461 A128168 A232823

Adjacent sequences:  A243387 A243388 A243389 * A243391 A243392 A243393

KEYWORD

nonn,base

AUTHOR

Colin Barker, Jun 04 2014

STATUS

approved

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Last modified August 1 20:40 EDT 2021. Contains 346402 sequences. (Running on oeis4.)