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A195335
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a(n) is the smallest Xmas tree prime with a(n-1) as a prefix (starting with 2).
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2
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2, 211, 211151, 2111511013, 211151101310867, 211151101310867100673, 2111511013108671006731000357, 211151101310867100673100035710000931, 211151101310867100673100035710000931100000213, 2111511013108671006731000357100009311000002131000000901, 211151101310867100673100035710000931100000213100000090110000001797
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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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]
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MAPLE
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read("transforms") ;
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;
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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