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

Author

Amarnath Murthy, Mar 02 2002

Keywords

• base
• nonn
• fini
• full

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

Examples

			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
		

Crossrefs

Cf. A012884, A062115, A202262.

Programs

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 *)

Extensions

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