# A113584

Hans Havermann pxp at rogers.com
Wed Nov 9 19:49:11 CET 2005

```> %I A113584
> %S A113584 3,7,3,3,61
> %N A113584 Beginning with 3 least prime so that concatenation of
> first n terms and its digit reversal both are prime.
> %C A113584 Subsidiary sequence:Beginning with 3, least number
> ( need not be prime) so that concatenation of first n terms and its
> digit reversal both are prime.
> %e A113584 3,37,373,3733,373361,... as well as
> 3,73,373,3373,163373,... are all prime.
> %K A113584 base,more,nonn,new
> %O A113584 1,1
> %A A113584 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 06 2005

Alas, 163373 is not prime! For the first 100 terms, I get:

{3, 7, 3, 3, 43, 101, 19, 269, 1873, 41, 241, 3137, 139, 9011, 9187,
641, 29881, 12227, 3169, 13499, 8539, 7019, 19447, 12899, 73243,
124769, 1063, 37847, 127, 32321, 104287, 3407, 93553, 256643, 165469,
744659, 60217, 54773, 49297, 214457, 314077, 271409, 602383, 56921,
193051, 255383, 75991, 25667, 583147, 121019, 153649, 178439, 259657,
451499, 1849333, 58067, 1181767, 121169, 69691, 802073, 512251,
1178003, 982819, 542687, 2764711, 309059, 704161, 155381, 503827,
33749, 33199, 129587, 1118893, 966923, 46153, 751691, 3180757, 86531,
897049, 5738981, 1673719, 756053, 1236481, 754829, 1995481, 3029801,
1675789, 154043, 2568697, 988409, 2188267, 225479, 652369, 214691,
3262081, 94823, 5002519, 357293, 9219139, 617237}

Larger concatenations are probable primes only, of course. For the
suggested subsidiary sequence (terms are 'least number', instead of
'least prime'), I get:

{3, 1, 1, 21, 11, 43, 47, 157, 753, 51, 917, 273, 2409, 703, 413,
3729, 1153, 6243, 8789, 2307, 4477, 137, 403, 10649, 4617, 4533,
6133, 4721, 877, 2469, 5967, 1557, 1047, 38931, 15533, 6877, 23987,
4767, 18049, 1463, 118333, 27897, 25449, 8741, 24717, 108867, 9789,
6129, 73663, 27881, 36769, 119177, 3027, 6457, 145677, 143, 6729,
62419, 14261, 159661, 40961, 164713, 35619, 137211, 16017, 137,
93877, 53459, 37527, 37563, 43687, 97937, 73999, 92381, 52141, 81513,
37361, 85641, 265821, 721531, 84831, 124341, 230777, 18033, 10273,
51191, 34293, 164313, 96643, 16961, 84727, 95169, 200243, 53559,
269491, 162237, 256241, 152049, 228969, 376261}

Somewhat more constrained but, to me - appealing, would be to limit
oneself to terms that are 'least prime whose digit-reversal is also
prime' (A007500). For this, I get:

{3, 7, 3, 3, 79, 701, 157, 1103, 11959, 1901, 10273, 92753, 17047,
11909, 144973, 327251, 99289, 92831, 90373, 309671, 1149619, 745397,
1232083, 94793, 18481, 76607, 186649, 181421, 1657561, 3746111,
7067239, 324143, 3185263, 9457181, 1703413, 3517583, 72481, 12859481,
145603, 9682811, 3371101, 1603067, 1451557, 3351071, 7017697,
3930197, 7111537, 14343503, 3427309, 726911, 12067273, 10470329,
13928533, 1072859, 12523909, 10084673, 9607453, 1398521, 1315087,
10575767, 1676281, 1352441, 12724807, 18678263, 9529651, 14074301,
15618901, 14380823, 19106119, 1654217, 12679129, 14033729, 3653821,
39353843, 14799997, 30639953, 1370749, 9450803, 70358983, 1775309,
10900081, 7900163, 11879251, 37179899, 11291557, 78954521, 11718607,
110442641, 9204901, 12399983, 3716299, 33338153, 161388481, 16288781,
110256571, 95084933, 135469, 16439873, 15943729, 39229667}

```