OFFSET
1,1
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)
EXAMPLE
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.
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}]]
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Roger L. Bagula, Jun 11 2006
EXTENSIONS
Name edited by Rémy Sigrist, Oct 08 2017
a(39)-a(41) from Michael S. Branicky, Jul 11 2022
STATUS
approved