A068669 Noncomposite numbers in which every substring is noncomposite.

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

Offset

1,2

Comments

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

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]](* Jean-François 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