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Numbers n such that the index of the prime and the prime share some digit.
2

%I #7 Sep 14 2014 20:35:54

%S 7,11,13,14,18,23,29,30,31,32,33,34,37,38,41,52,54,55,56,62,63,73,74,

%T 75,78,80,81,82,83,84,92,94,95,97,100,103,105,107,109,110,112,113,114,

%U 115,116,121,125,126,127,128,129,130,131,132,133,135,136,137,138,139,140

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

%H Reinhard Zumkeller, <a href="/A119393/b119393.txt">Table of n, a(n) for n = 1..10000</a>

%F Intersection of A000027&A000040 which share a digit.

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

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

%o (Haskell)

%o import Data.List (intersect)

%o a119393 n = a119393_list !! (n-1)

%o a119393_list = filter

%o (\x -> not $ null $ show x `intersect` (show $ a000040 x)) [1..]

%o -- _Reinhard Zumkeller_, Sep 14 2014

%Y Cf. A000027, A000040, A243355 (complement).

%K nonn,base,less

%O 1,1

%A _Robert G. Wilson v_, Jul 25 2006