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A119680 Prime numbers obtained by inserting a 0 between each pair of adjacent digits of a prime number > 10.

%I A119680 #20 Jul 11 2022 19:55:02
%S A119680 101,103,107,109,307,401,503,509,601,607,701,709,809,907,10007,10009,
%T A119680 10103,10301,10501,10607,10709,10903,10909,20101,20507,20707,20903,
%U A119680 30103,30307,30509,30703,30803,30809,40009,40507,40709,50707,50909,60103,60107,60509
%N A119680 Prime numbers obtained by inserting a 0 between each pair of adjacent digits of a prime number > 10.
%C A119680 From _Rémy Sigrist_, Oct 08 2017: (Start)
%C A119680 See A159236 for the original prime numbers.
%C A119680 The least prime numbers > 10 remaining prime during exactly k iterations of the operation of inserting a 0 between each pair of adjacent digits are, for small values of k:
%C A119680 k prime
%C A119680 - -----
%C A119680 0 23
%C A119680 1 11
%C A119680 2 19
%C A119680 3 17
%C A119680 4 220333
%C A119680 5 8677267
%C A119680 (End)
%e A119680 The first four terms arise from 11 -> 101, 13 -> 103, 17 -> 107, 19 -> 109.
%e A119680 23 -> 203 is not prime, so 203 is not a term.
%t A119680 a = Table[Table[Mod[Floor[Prime[m]/10^n], 10], {n, 4, 0, -1}], {m, 5, 200}]; Dimensions[a] b = Table[Sum[(If[Mod[n - 1, 2] == 0, a[[m, 1 + Floor[(n - 1)/2]]], 0])*10^(9 - n), {n, 1, 9}], {m, 1, 195}]; c = Flatten[Table[If[PrimeQ[b[[m]]], b[[m]], {}], {m, 1, 195}]]
%o A119680 (PARI) forprime (p=10, 599, if (isprime(pp=fromdigits(digits(p), 100)), print1 (pp ", "))) \\ _Rémy Sigrist_, Oct 08 2017
%o A119680 (Python)
%o A119680 from itertools import count, islice
%o A119680 from sympy import isprime, nextprime
%o A119680 def ok(n):
%o A119680     return n > 10 and isprime(n) and isprime(int("0".join(list(str(n)))))
%o A119680 def agen():
%o A119680     p = 11
%o A119680     while True:
%o A119680         t = int("0".join(list(str(p))))
%o A119680         if isprime(t): yield t
%o A119680         p = nextprime(p)
%o A119680 print(list(islice(agen(), 50))) # _Michael S. Branicky_, Jul 11 2022
%Y A119680 Cf. A159236.
%K A119680 nonn,base
%O A119680 1,1
%A A119680 _Roger L. Bagula_, Jun 11 2006
%E A119680 Name edited by _Rémy Sigrist_, Oct 08 2017
%E A119680 a(39)-a(41) from _Michael S. Branicky_, Jul 11 2022