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

101, 103, 107, 109, 307, 401, 503, 509, 601, 607, 701, 709, 809, 907, 10007, 10009, 10103, 10301, 10501, 10607, 10709, 10903, 10909, 20101, 20507, 20707, 20903, 30103, 30307, 30509, 30703, 30803, 30809, 40009, 40507, 40709, 50707, 50909, 60103, 60107, 60509

Offset: 1

Author

Roger L. Bagula, Jun 11 2006

Keywords

• nonn
• base

Comments

From Rémy Sigrist, Oct 08 2017: (Start)

See A159236 for the original prime numbers.

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:

k prime

- -----

0 23

1 11

2 19

3 17

4 220333

5 8677267

(End)

Examples

			The first four terms arise from 11 -> 101, 13 -> 103, 17 -> 107, 19 -> 109.
23 -> 203 is not prime, so 203 is not a term.
		

Crossrefs

Cf. A159236.

Programs

Mathematica

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}]]

PARI

forprime (p=10, 599, if (isprime(pp=fromdigits(digits(p), 100)), print1 (pp ", "))) \\ Rémy Sigrist, Oct 08 2017

Python

from itertools import count, islice
from sympy import isprime, nextprime
def ok(n):
    return n > 10 and isprime(n) and isprime(int("0".join(list(str(n)))))
def agen():
    p = 11
    while True:
        t = int("0".join(list(str(p))))
        if isprime(t): yield t
        p = nextprime(p)
print(list(islice(agen(), 50))) # Michael S. Branicky, Jul 11 2022

Extensions

Name edited by Rémy Sigrist, Oct 08 2017

a(39)-a(41) from Michael S. Branicky, Jul 11 2022