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.

13, 21, 31, 33, 37, 49, 63, 67, 69, 79, 81, 91, 99, 107, 131, 139, 143, 157, 161, 181, 187, 193, 197, 203, 211, 221, 227, 233, 251, 253, 259, 277, 281, 299, 311, 313, 323, 331, 337, 367, 371, 373, 377, 379, 403, 421, 427, 451, 461, 467, 479

Offset: 1

Author

Bernard Schott, Jan 10 2020

Keywords

• nonn
• base

Comments

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.

Examples

			281 gives 2(1)8(2)1 = 21821 that is prime, hence 281 is a term.
1027 gives 1(1)0(2)2(3)7 = 1102237 that is prime, hence 1027 is another term.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050711, A050712, A050713, A050714.

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

Programs

Mathematica

seqQ[n_] := PrimeQ @ FromDigits @ Flatten @ IntegerDigits @ Riffle[(d = IntegerDigits[n]), Range[Length[d] - 1]]; Select[Range[10,480], seqQ] (* Amiram Eldar, Jan 10 2020 *)

Python

from sympy import isprime
def ok(n):
    if n < 10: return False
    s = str(n)
    shuffle = list(map(str, ((i+1)//2 for i in range(2*len(s)-1))))
    shuffle[0::2] = [s[i] for i in range(len(s))]
    return isprime(int("".join(shuffle)))
print(list(filter(ok, range(480)))) # Michael S. Branicky, Jul 18 2021