A012884 Numbers such that every prefix and suffix is 1 or a prime.

1, 2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 113, 131, 137, 173, 197, 311, 313, 317, 373, 797, 1373, 1997, 3137, 3797, 7331, 73331, 739397

Offset: 1

Author

Larry Calmer (larry(AT)wri.com), Simon Plouffe

Keywords

• nonn
• fini
• full
• nice
• base

Comments

Last term is 739397 (confirmed by David W. Wilson).

Intersection of A012883 and A143390. [Reinhard Zumkeller, Aug 13 2008]

Crossrefs

Cf. A068669.

Programs

Mathematica

prQ[n_] := n == 1 || PrimeQ[n];
okQ[n_] := Module[{dd, nd}, dd = IntegerDigits[n]; nd = Length[dd]; AllTrue[Range[nd], prQ@ FromDigits@ Take[dd, #]&] && AllTrue[Range[nd-1], prQ@ FromDigits@ Drop[dd, #]&]];
{1}~Join~Select[Prime@Range[60000], okQ] (* Jean-François Alcover, Nov 20 2019 *)