

A195335


a(n) is the smallest Xmas tree prime with a(n1) as a prefix (starting with 2).


2



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

Table of n, a(n) for n=1..11.
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(n1) ;
for nxt from 10^(n1) to 10^n1 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**(n1))
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

Cf. A000217.
Sequence in context: A107612 A068814 A215641 * A090560 A181903 A345397
Adjacent sequences: A195332 A195333 A195334 * A195336 A195337 A195338


KEYWORD

nonn,base


AUTHOR

Kausthub Gudipati, Sep 16 2011


EXTENSIONS

Name corrected by Michael S. Branicky, Dec 26 2020


STATUS

approved



