A331116 - OEIS

%I #25 Jul 19 2021 01:21:49

%S 13,21,31,33,37,49,63,67,69,79,81,91,99,107,131,139,143,157,161,181,

%T 187,193,197,203,211,221,227,233,251,253,259,277,281,299,311,313,323,

%U 331,337,367,371,373,377,379,403,421,427,451,461,467,479

%N 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 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 Giovanni Resta, <a href="/A331116/b331116.txt">Table of n, a(n) for n = 1..10000</a>

%e 281 gives 2(1)8(2)1 = 21821 that is prime, hence 281 is a term.

%e 1027 gives 1(1)0(2)2(3)7 = 1102237 that is prime, hence 1027 is another term.

%t 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 (Python)

%o from sympy import isprime

%o def ok(n):

%o     if n < 10: return False

%o     s = str(n)

%o     shuffle = list(map(str, ((i+1)//2 for i in range(2*len(s)-1))))

%o     shuffle[0::2] = [s[i] for i in range(len(s))]

%o     return isprime(int("".join(shuffle)))

%o print(list(filter(ok, range(480)))) # _Michael S. Branicky_, Jul 18 2021

%Y Cf. A050711, A050712, A050713, A050714.

%Y Cf. A050715, A050716, A050717, A050718, A050719.

%K nonn,base

%O 1,1

%A _Bernard Schott_, Jan 10 2020