A243355 -id:A243355 - cp's OEIS frontend

A119393 Numbers n such that the index of the prime and the prime share some digit.

7, 11, 13, 14, 18, 23, 29, 30, 31, 32, 33, 34, 37, 38, 41, 52, 54, 55, 56, 62, 63, 73, 74, 75, 78, 80, 81, 82, 83, 84, 92, 94, 95, 97, 100, 103, 105, 107, 109, 110, 112, 113, 114, 115, 116, 121, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140

Offset: 1

Robert G. Wilson v, Jul 25 2006

			7 is a member since the seventh prime is 17 with the index and the prime sharing the digit 7.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000027, A000040, A243355 (complement).

import Data.List (intersect)
a119393 n = a119393_list !! (n-1)
a119393_list = filter
   (\x -> not $ null $ show x `intersect` (show $ a000040 x)) [1..]
-- Reinhard Zumkeller, Sep 14 2014

Select[Range@140, Intersection[IntegerDigits@#, IntegerDigits@ Prime@# ] != {} &]

Intersection of A000027&A000040 which share a digit.

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

Original entry on oeis.org

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

Colin Barker, Jun 04 2014

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

			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.

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

Cf. A000010, A000040, A243355, A243356.

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 *)

{ 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 }

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

cp's OEIS Frontend

A119393 Numbers n such that the index of the prime and the prime share some digit.

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