A243390 - OEIS

%I #25 Sep 06 2020 06:41:40

%S 2,3,4,5,6,8,9,10,12,15,16,20,22,39,44,46,48,65,66,77,87,93,99,123,

%T 134,146,154,165,230,246,430,441,446,494,522,528,552,555,566,622,662,

%U 711,737,738,740,825,855,984,1155,1160,1170,1180,1214,2230,5055,8878

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

%C a(95) > 10^10 if it exists. - _David A. Corneth_, Aug 25 2020

%H David A. Corneth, <a href="/A243390/b243390.txt">Table of n, a(n) for n = 1..94</a>

%e 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.

%t 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 *)

%o (PARI)

%o { s=[];

%o   for(n=1, 50000,

%o     u=vecsort(digits(n),,8);

%o     v=vecsort(digits(prime(n)),,8);

%o     w=vecsort(digits(eulerphi(n)),,8);

%o     if(setintersect(u, v)==[]&&setintersect(u, w)==[]&&setintersect(v, w)==[],

%o       s=concat(s, n)

%o     )

%o   );

%o   s }

%o (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

%Y Cf. A000010, A000040, A243355, A243356.

%K nonn,base

%O 1,1

%A _Colin Barker_, Jun 04 2014