

A068669


Noncomposite numbers in which every substring is noncomposite.


8



1, 2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 113, 131, 137, 173, 311, 313, 317, 373, 1373, 3137
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OFFSET

1,2


COMMENTS

It is easy to see that this sequence is complete  the only potential 5digit candidate 31373 is not prime.  Tanya Khovanova, Dec 09 2006


LINKS

Table of n, a(n) for n=1..24.


EXAMPLE

137 is a member as all the substrings, i.e. 1, 3, 7, 13, 37, 137, are noncomposite.
All substrings of 3137 are noncomposite numbers: 1, 3, 7, 13, 37, 137, 313, 3137.  Jaroslav Krizek, Dec 25 2011


MATHEMATICA

noncompositeQ[n_] := n == 1  PrimeQ[n]; Reap[ Do[ id = IntegerDigits[n]; lid = Length[id]; test = And @@ noncompositeQ /@ FromDigits[#, 10]& /@ Flatten[ Table[ Take[id, {i, j}], {i, 1, lid}, {j, i, lid}], 1]; If[test, Sow[n]], {n, Join[{1}, Prime /@ Range[10000]]}]][[2, 1]](* JeanFrançois Alcover, May 09 2012 *)


CROSSREFS

Cf. A012884, A062115, A202262.
Sequence in context: A160337 A190222 A012884 * A316412 A100553 A175584
Adjacent sequences: A068666 A068667 A068668 * A068670 A068671 A068672


KEYWORD

base,nonn,fini,full


AUTHOR

Amarnath Murthy, Mar 02 2002


EXTENSIONS

1 added following a redefinition by Jaroslav Krizek.  R. J. Mathar, Jan 20 2012


STATUS

approved



