|
|
A084366
|
|
Numbers n such that the n-th prime number has an odd number of digits and becomes composite if the central digit is removed.
|
|
0
|
|
|
47, 49, 53, 54, 55, 58, 59, 60, 65, 70, 71, 72, 74, 75, 76, 77, 80, 81, 85, 87, 92, 95, 98, 100, 101, 102, 105, 106, 107, 112, 114, 117, 119, 120, 122, 124, 129, 134, 138, 139, 141, 142, 144, 148, 151, 152, 154, 156, 157, 158, 160, 162, 164, 166, 167
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
The 47th prime is 211, omitting the central digit yields 21, which is composite. The 59th prime is 277, omitting the central digit yields 27, which is composite.
|
|
MATHEMATICA
|
Select[Range[5, 1500], OddQ[Length[IntegerDigits[Prime[ # ]]]] && Not[PrimeQ[FromDigits[Drop[IntegerDigits[Prime[ # ]], {(Length[IntegerDigits[Prime[ # ]]] + 1)/2}]]]] &]
ondQ[n_]:=Module[{idn=IntegerDigits[Prime[n]], len}, len=Length[idn]; OddQ[ len] &&CompositeQ[FromDigits[Drop[idn, {(len+1)/2}]]]]; Select[Range[200], ondQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 02 2018 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn,less
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|