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Numbers k such that the concatenation of all nonprime natural numbers up to k with decreasing order is prime.
3

%I #19 Nov 26 2024 02:14:11

%S 4,5,6,7,8,9,26,1752,1753

%N Numbers k such that the concatenation of all nonprime natural numbers up to k with decreasing order is prime.

%C If k is in the sequence and k+1 is prime then k+1 is also in the sequence. Next term is greater than 5450 and the prime corresponding to the next term has more than 18000 digits. Number of digits of primes corresponding to the nine known terms of the sequence are respectively 2,2,3,3,4,5,29,5010 & 5010.

%C a(10) > 20000. - _Michael S. Branicky_, Nov 25 2024

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8. Primes by Listing</a>, The Prime Puzzles & Problems connection.

%e 9 is in the sequence because all nonprime natural numbers up to 9 are 1,4,6,8 & 9 and 98641 is prime.

%t Do[If[PrimeQ[(v={};Do[If[ !PrimeQ[n+1-j], v=Join[v, IntegerDigits [n+1-j]]], {j, n}];FromDigits[v])], Print[n]], {n, 5450}]

%Y Cf. A046284, A099071.

%K base,more,nonn

%O 1,1

%A _Farideh Firoozbakht_, Nov 04 2004