A099071 Composite numbers k such that the concatenation of all nonprime positive integers up to k in decreasing order is prime.

4, 6, 8, 9, 26, 1752

Offset

1,1

Comments

The terms of this sequence are composite terms of the sequence A099070 with the 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, and 5010.

Links

Table of n, a(n) for n=1..6.

Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles and Problems Connection.

Example

26 is a term: 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+1-j], v=Join[v, IntegerDigits[n+1-j]]], {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 A372408

Adjacent sequences: A099068 A099069 A099070 * A099072 A099073 A099074

Keyword

base,more,nonn,nice

Author

Farideh Firoozbakht, Nov 06 2004

Status

approved