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

1,1

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.

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A050711, A050712, A050713, A050714.

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

Sequence in context: A195375 A128819 A165955 * A050711 A282844 A020440

Adjacent sequences: A331113 A331114 A331115 * A331117 A331118 A331119

Keyword

nonn,base

Author

Bernard Schott, Jan 10 2020

Status

approved