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%I #14 Jul 16 2021 11:39:31
%S 2,3,7,24,76,1100
%N Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.
%C A100003(n) = prime(a(n)). Next term is greater than 4500 and the prime corresponding to the next term has more than 21000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 1, 2, 9, 43, 198, and 4202. There is no known prime formed by concatenation of the first k odd primes in increasing order for 1 < k < 2250.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8. Primes by Listing</a>, The Prime Puzzles and Problems Connection.
%e 7 is in the sequence because the first 6 odd primes are 3,5,7,11,13,17 and 17.13.11.7.5.3 is prime (dot between numbers means concatenation).
%t Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[n]], {n, 2, 4500}]
%t Select[Range[1100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Reverse[ Prime[ Range[ 2,#]]]]]]&] (* _Harvey P. Dale_, Nov 12 2017 *)
%Y Cf. A046035, A099070, A099071.
%K base,more,nonn,nice
%O 1,1
%A _Farideh Firoozbakht_, Nov 06 2004