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.
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*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

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

***

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".

***

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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