

A099071


Composite numbers n such that the concatenation of all nonprime natural numbers up to n in decreasing order is prime.


3




OFFSET

1,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..6.
C. Rivera, Primes by Listing.


EXAMPLE

26 is in the sequence because 26 is composite; nonprimes
up to 26 are 1,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26
and 26252422212018161514121098641 is prime.


MATHEMATICA

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}]
cnpQ[n_]:=PrimeQ[FromDigits[Flatten[IntegerDigits/@Select[Range[n, 1, 1], !PrimeQ[#]&]]]]; Select[Range[1800], !PrimeQ[#]&&cnpQ[#]&] (* Harvey P. Dale, Jul 19 2020 *)


CROSSREFS

Cf. A099070, A100003, A046284.
Sequence in context: A161732 A066307 A287198 * A156673 A073866 A202260
Adjacent sequences: A099068 A099069 A099070 * A099072 A099073 A099074


KEYWORD

base,more,nonn,nice


AUTHOR

Farideh Firoozbakht, Nov 06 2004


STATUS

approved



