Problems & Puzzles: Puzzles

Puzzle 724. Extending the OEIS sequence A229908 Here you are asked just to extend the sequence A229908 beyond the prime 1139917333 which has 43 embedded primes, reading forward and backward. Q. Send your next terms for this sequence. ____ *Last time note: In my OEIS sequence A229908 a made a mistake when I copied the results of my search. This is the correct one:   1 2   2 13   3 13   4 37   5 113   6 113   7 137   8 1237   9 1373   10 1733   11 1733   12 11317   13 11731   14 12713   15 19973   16 91733   17 113173   18 113371   19 113371 This term was missing 20 173347   21 991733   22 1123379   23 1134673   24 1137991   25 1237199   26 2333719   27 7433719   28 11133719   29 11399173   30 11399173   31 11791733   32 37914713   33 97433719   34 113217397   35 113217397   36 113337199   37 113337199   38 113337199   39 1113371999   40 1113371999   41 1113991733   42 1139917321   43 1139917321   44 1139917333

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Contributions came from Emmanuel Vantieghem, Abhiram R Devesh and Giovanni Resta
 

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Emmanuel wrote:

This is, in my humble opinion, how A229908 should be extended :
 

  n     A229908(n)       k

  45   1139917333     45

  46   10333719713   46

  47   11329715377   48

  48   11329715377   48

  49   11333719967   49

 

The next term is > 14*10^9

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Abhiram wrote:

45:1139917333
46:11299173359 (possible smallest number with 46 embedded primes)
In order to cover a good range, i scanned for numbers having all odd digits with atmost a single "2".
 

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Giovanni wrote:

I stopped my search at 3.5*10^12. I found 65 terms, which are:

2,13,13,37,113,113,137,1237,1373,1733,1733,11317,11731,12713,19973,91733,113173,
113371,113371,173347,991733,1123379,1134673,1137991,1237199,2333719,7433719,11133719,
11399173,11399173,11791733,37914713,97433719,113217397,113217397,113337199,113337199,
113337199,1113371999,1113371999,1113991733,1139917321,1139917321,1139917333,1139917333,
10333719713,11329715377,11329715377,11333719967,17333911597,17333911597,93119333719,
113173335923,113217519733,113297193377,121139917333,127951193371,139329991733,139329991733,
139329991733,795119333719,1133297193337,1133297193373,1395119333719,3337199311939

The 65 primes embedded in 3337199311939 are

3, 7, 11, 13, 17, 19, 31, 37, 71, 73, 113, 139, 173, 193, 199, 311,
337, 719, 733, 911, 991, 1193, 1399, 1733, 1993, 3119, 3371, 3719,
3911, 7333, 9173, 9311, 9391, 9931, 11399, 11939, 17333, 31193,
37199, 39113, 71993, 91139, 91733, 93911, 99173, 333719, 399173,
917333, 931193, 991733, 1139917, 3337199, 3371993, 9391139, 11399173,
39917333, 99311939, 113991733, 371993119, 1139917333, 33371993119,
37199311939, 39113991733, 939113991733, and 3337199311939.

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