%I
%S 4,6,8,9,26,1752
%N Composite numbers n such that the concatenation of all nonprime natural numbers up to n in decreasing order is prime.
%C The terms of this sequence are composite terms of the sequence A099070 with same order. Next term is greater than 6000 and the prime corresponding to the next term has more than 20000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 2,3,4,5,29 & 5010.
%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Primes by Listing</a>.
%e 26 is in the sequence because 26 is composite; nonprimes
%e up to 26 are 1,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26
%e and 26252422212018161514121098641 is prime.
%t Do[If[ !PrimeQ[n]&&PrimeQ[(v={};Do[If[ !PrimeQ[n+1j], v=Join[v, IntegerDigits[n+1j]]], {j, n}];FromDigits[v])], Print[n]], {n, 6013}]
%Y Cf. A099070, A100003, A046284.
%K base,more,nonn,nice
%O 1,1
%A _Farideh Firoozbakht_, Nov 06 2004
