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
Examples
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.
Links
- David A. Corneth, Table of n, a(n) for n = 1..94
Programs
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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 *) -
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
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