A226108 Primes remaining prime if all but two digits are deleted.

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 131, 137, 173, 179, 197, 311, 317, 431, 617, 719, 1117, 1171, 4111, 11113, 11117, 11119, 11131, 11171, 11173, 11197, 11311, 11317, 11719, 11731, 13171, 13711, 41113

Offset: 1

Author

Tim Cieplowski, May 26 2013

Keywords

• nonn
• base

Comments

Subsequence of A069488.

Examples

			For a(3)=137, all pairs of two digits (in their original order) 13, 17, and 37 are prime.
		

References

• C. Caldwell, Truncatable primes, J. Recreational Math., 19:1 (1987) 30-33.

Links

• Tim Cieplowski, Table of n, a(n) for n = 1..2720
• P. Ballew, Knockout Primes and a new notation, May 17, 2013
• C. Caldwell, The Prime Glossary: Deletable Prime

Crossrefs

Cf. A019546, A051362, A069488.

Programs

Mathematica

testQ[n_] := n > 9 && Catch[Block[{d = IntegerDigits@n}, Do[If[! PrimeQ[ d[[j]] + 10*d[[i]]], Throw@False], {j, 2, Length@d}, {i, j-1}]; True]]; Select[Prime@ Range[10^5], testQ] (* Giovanni Resta, May 28 2013 *)