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A068645 Primes in which a string of 3's is sandwiched between two 1's.

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%I A068645 #22 Jan 27 2023 13:34:41
%S A068645 11,131,13331,1333331,
%T A068645 13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331
%N A068645 Primes in which a string of 3's is sandwiched between two 1's.
%C A068645 a(5) consists of 93 and a(6) consists of 159 3's sandwiched between two 1's. - _Sascha Kurz_, Mar 26 2002
%C A068645 a(8) has 1471 digits. - _Michael S. Branicky_, Jan 27 2023
%H A068645 Michael S. Branicky, <a href="/A068645/b068645.txt">Table of n, a(n) for n = 1..7</a>
%H A068645 Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp131">PDP Reference Table - 131</a>.
%H A068645 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/13331.htm#prime">Prime numbers of the form 133...331</a>.
%H A068645 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%t A068645  Select[Flatten[Table[10*FromDigits[PadRight[{1},n,3]]+1,{n,120}]],PrimeQ] (* _Harvey P. Dale_, Aug 09 2020 *)
%o A068645 (Python)
%o A068645 from sympy import isprime
%o A068645 from itertools import count, islice
%o A068645 def agen(): yield from (t for i in count(0) if isprime(t:=int("1" + "3"*i + "1")))
%o A068645 print(list(islice(agen(), 7))) # _Michael S. Branicky_, Jan 27 2023
%Y A068645 Cf. A056244, A082697.
%K A068645 base,nonn
%O A068645 1,1
%A A068645 _Amarnath Murthy_, Feb 28 2002
%E A068645 More terms from _Sascha Kurz_, Mar 26 2002
%E A068645 Edited by _Ray Chandler_, Nov 04 2014