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A099073
Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.
1
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
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
KEYWORD
base,more,nonn,nice
AUTHOR
Farideh Firoozbakht, Nov 06 2004
STATUS
approved