A084366 - OEIS

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.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..55.

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

Sequence in context: A345502 A249372 A042103 * A257785 A234023 A128940

Adjacent sequences: A084363 A084364 A084365 * A084367 A084368 A084369

KEYWORD

base,nonn,less

AUTHOR

Zak Seidov, Jun 22 2003

EXTENSIONS

Edited by Stefan Steinerberger, Sep 05 2007

STATUS

approved