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A195335 a(n) is the smallest Xmas tree prime with a(n-1) as a prefix (starting with 2). 2
2, 211, 211151, 2111511013, 211151101310867, 211151101310867100673, 2111511013108671006731000357, 211151101310867100673100035710000931, 211151101310867100673100035710000931100000213, 2111511013108671006731000357100009311000002131000000901, 211151101310867100673100035710000931100000213100000090110000001797 (list; graph; refs; listen; history; text; internal format)
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(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

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

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Last modified February 5 03:44 EST 2023. Contains 360082 sequences. (Running on oeis4.)