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A068669
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Noncomposite numbers in which every substring is noncomposite.
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8
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1, 2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 113, 131, 137, 173, 311, 313, 317, 373, 1373, 3137
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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It is easy to see that this sequence is complete - the only potential 5-digit candidate 31373 is not prime. - Tanya Khovanova, Dec 09 2006
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LINKS
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Table of n, a(n) for n=1..24.
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EXAMPLE
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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
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MATHEMATICA
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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]](* Jean-François Alcover, May 09 2012 *)
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CROSSREFS
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Cf. A012884, A062115, A202262.
Sequence in context: A160337 A190222 A012884 * A316412 A100553 A175584
Adjacent sequences: A068666 A068667 A068668 * A068670 A068671 A068672
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KEYWORD
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base,nonn,fini,full
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AUTHOR
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Amarnath Murthy, Mar 02 2002
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EXTENSIONS
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1 added following a redefinition by Jaroslav Krizek. - R. J. Mathar, Jan 20 2012
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STATUS
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approved
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