OFFSET
1,1
COMMENTS
A Xmas tree prime is a prime which is a concatenation of a prime with a single digit, a prime with two digits, a prime with three digits, a prime with four digits etc. By definition, the number of digits is a triangular number (A000217). Leading zeros are not allowed for any of the primes.
LINKS
Terry Trotter, Xmas tree primes [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]
MAPLE
read("transforms") ;
A195335 := proc(n)
option remember;
local prev, nxt, a ;
if n =1 then
2;
else
prev := procname(n-1) ;
for nxt from 10^(n-1) to 10^n-1 do
if isprime(nxt) then
a := digcat2(prev, nxt) ;
if isprime(a) then
return a ;
end if;
end if;
end do:
return -1 ;
end if;
end proc: # R. J. Mathar, Sep 20 2011
PROG
(Python)
from sympy import isprime, nextprime
def alst(nn):
alst, astr = [2], "2"
for n in range(2, nn+1):
p = nextprime(10**(n-1))
while not isprime(int(astr + str(p))): p = nextprime(p)
alst.append(int(astr + str(p))); astr += str(p)
return alst
print(alst(11)) # Michael S. Branicky, Dec 26 2020
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Kausthub Gudipati, Sep 16 2011
EXTENSIONS
Name corrected by Michael S. Branicky, Dec 26 2020
STATUS
approved