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%I #32 Dec 27 2020 01:57:59
%S 2,211,211151,2111511013,211151101310867,211151101310867100673,
%T 2111511013108671006731000357,211151101310867100673100035710000931,
%U 211151101310867100673100035710000931100000213,2111511013108671006731000357100009311000002131000000901,211151101310867100673100035710000931100000213100000090110000001797
%N a(n) is the smallest Xmas tree prime with a(n-1) as a prefix (starting with 2).
%C 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.
%H Terry Trotter, <a href="https://web.archive.org/web/20160629211025/http://trottermath.net/numtrivia/potpourri.html">Xmas tree primes</a> [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]
%p read("transforms") ;
%p A195335 := proc(n)
%p option remember;
%p local prev,nxt,a ;
%p if n =1 then
%p 2;
%p else
%p prev := procname(n-1) ;
%p for nxt from 10^(n-1) to 10^n-1 do
%p if isprime(nxt) then
%p a := digcat2(prev,nxt) ;
%p if isprime(a) then
%p return a ;
%p end if;
%p end if;
%p end do:
%p return -1 ;
%p end if;
%p end proc: # _R. J. Mathar_, Sep 20 2011
%o (Python)
%o from sympy import isprime, nextprime
%o def alst(nn):
%o alst, astr = [2], "2"
%o for n in range(2, nn+1):
%o p = nextprime(10**(n-1))
%o while not isprime(int(astr + str(p))): p = nextprime(p)
%o alst.append(int(astr + str(p))); astr += str(p)
%o return alst
%o print(alst(11)) # _Michael S. Branicky_, Dec 26 2020
%Y Cf. A000217.
%K nonn,base
%O 1,1
%A _Kausthub Gudipati_, Sep 16 2011
%E Name corrected by _Michael S. Branicky_, Dec 26 2020
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