|
|
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
|
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|