A178504 Numbers n such that n^2 + 13 is an emirp.

2, 10, 12, 18, 44, 60, 88, 108, 110, 114, 116, 122, 192, 198, 282, 380, 446, 574, 588, 604, 612, 618, 838, 840, 864, 970, 1032, 1068, 1104, 1148, 1186, 1228, 1258, 1314, 1368, 1384, 1390, 1412, 1754, 1888, 1894, 1930, 2658, 2660, 2728, 2784, 2804

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 29 2010

Keywords

• base
• nonn

Comments

A decimal emirp/mirp ("prime" / (German) "prim", spelled backwards) is defined as a prime number p whose reversal R(p) is also prime, but which is not a palindromic prime.

Examples

			2^2 + 13 = 17 = prime(7), 71 = prime(20), so 2 is in the sequence.
10^2 + 13 = 113 = prime(30), 311 = prime(64), so 10 is in the sequence.
28^2 + 13 = 797, which is a palindromic prime, so 28 is not in the sequence.
		

References

• W. W. R. Ball, H. S. M. Coxeter: Mathematical Recreations and Essays, 13th edition, Dover Publications, 2010
• H. Steinhaus: Kaleidoskop der Mathematik, VEB Dt. Verl. d. Wissenschaften, Berlin, 1959

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..8000

Crossrefs

Subsequence of A113536.

Cf. A138375, A176978, A178044.

Programs

Mathematica

fQ[n_] := If[ PrimeQ[n^2 + 13], Block[{id = IntegerDigits[n^2 + 13]}, rid = Reverse@ id; PrimeQ@ FromDigits@ rid && rid != id]]; Select[ Range@ 3000, fQ] (* Robert G. Wilson v, Jul 26 2010 *)

Extensions

More terms from Robert G. Wilson v, Jul 26 2010