A099073 Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.

2, 3, 7, 24, 76, 1100

Offset

1,1

Comments

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.

Links

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

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

Example

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).

Mathematica

Do[If[PrimeQ[(v={}; Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}]; FromDigits[v])], Print[n]], {n, 2, 4500}]
Select[Range[1100], PrimeQ[FromDigits[Flatten[IntegerDigits/@ Reverse[ Prime[ Range[ 2, #]]]]]]&] (* Harvey P. Dale, Nov 12 2017 *)

Crossrefs

Cf. A046035, A099070, A099071.

Sequence in context: A102710 A048824 A355015 * A129724 A358496 A308161

Adjacent sequences: A099070 A099071 A099072 * A099074 A099075 A099076

Keyword

base,more,nonn,nice

Author

Farideh Firoozbakht, Nov 06 2004

Status

approved