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A099071 Composite numbers k such that the concatenation of all nonprime positive integers up to k in decreasing order is prime. 3
4, 6, 8, 9, 26, 1752 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A161732 A066307 A287198 * A156673 A073866 A202260
KEYWORD
base,more,nonn,nice
AUTHOR
Farideh Firoozbakht, Nov 06 2004
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)