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A331116 Inserting a digit '1' between the first two adjacent digits of k, then inserting a digit '2' between the two following adjacent digits of k, ..., then inserting the integer '10' between the tenth and the eleventh digits of k, ... produces a prime number.

%I A331116 #25 Jul 19 2021 01:21:49
%S A331116 13,21,31,33,37,49,63,67,69,79,81,91,99,107,131,139,143,157,161,181,
%T A331116 187,193,197,203,211,221,227,233,251,253,259,277,281,299,311,313,323,
%U A331116 331,337,367,371,373,377,379,403,421,427,451,461,467,479
%N A331116 Inserting a digit '1' between the first two adjacent digits of k, then inserting a digit '2' between the two following adjacent digits of k, ..., then inserting the integer '10' between the tenth and the eleventh digits of k, ... produces a prime number.
%C A331116 Inspired by the sequences A050711 to A050719, so the first 13 terms are the first 13 terms of A050711, then a(14) = 107 because 1(1)0(2)7 gives 11027 which is a prime.
%H A331116 Giovanni Resta, <a href="/A331116/b331116.txt">Table of n, a(n) for n = 1..10000</a>
%e A331116 281 gives 2(1)8(2)1 = 21821 that is prime, hence 281 is a term.
%e A331116 1027 gives 1(1)0(2)2(3)7 = 1102237 that is prime, hence 1027 is another term.
%t A331116 seqQ[n_] := PrimeQ @ FromDigits @ Flatten @ IntegerDigits @ Riffle[(d = IntegerDigits[n]), Range[Length[d] - 1]]; Select[Range[10,480], seqQ] (* _Amiram Eldar_, Jan 10 2020 *)
%o A331116 (Python)
%o A331116 from sympy import isprime
%o A331116 def ok(n):
%o A331116     if n < 10: return False
%o A331116     s = str(n)
%o A331116     shuffle = list(map(str, ((i+1)//2 for i in range(2*len(s)-1))))
%o A331116     shuffle[0::2] = [s[i] for i in range(len(s))]
%o A331116     return isprime(int("".join(shuffle)))
%o A331116 print(list(filter(ok, range(480)))) # _Michael S. Branicky_, Jul 18 2021
%Y A331116 Cf. A050711, A050712, A050713, A050714.
%Y A331116 Cf. A050715, A050716, A050717, A050718, A050719.
%K A331116 nonn,base
%O A331116 1,1
%A A331116 _Bernard Schott_, Jan 10 2020