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A195335 Smallest Xmas tree prime with k digits where k is the n-th triangular number. 2
2, 211, 211151, 2111511013, 211151101310867, 211151101310867100673, 2111511013108671006731000357, 211151101310867100673100035710000931, 211151101310867100673100035710000931100000213, 2111511013108671006731000357100009311000002131000000901, 211151101310867100673100035710000931100000213100000090110000001797 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..11.

Terry Trotter, Xmas tree primes


read("transforms") ;

A195335 := proc(n)

        option remember;

        local prev, nxt, a ;

        if n =1 then



                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


Cf. A000217.

Sequence in context: A068814 A170920 A215641 * A090560 A181903 A078280

Adjacent sequences:  A195332 A195333 A195334 * A195336 A195337 A195338




Kausthub Gudipati, Sep 16 2011



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Last modified December 21 19:36 EST 2014. Contains 252325 sequences.