A195335 a(n) is the smallest Xmas tree prime with a(n-1) as a prefix (starting with 2).

2, 211, 211151, 2111511013, 211151101310867, 211151101310867100673, 2111511013108671006731000357, 211151101310867100673100035710000931, 211151101310867100673100035710000931100000213, 2111511013108671006731000357100009311000002131000000901, 211151101310867100673100035710000931100000213100000090110000001797

Offset: 1

Author

Kausthub Gudipati, Sep 16 2011

Keywords

• nonn
• base

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

Crossrefs

Cf. A000217.

Programs

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

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

Extensions

Name corrected by Michael S. Branicky, Dec 26 2020