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A309191 a(n) is the least prime such that each concatenation of 1 <= k <= n consecutive primes beginning with a(n) is prime, or 0 if no such prime exists. 2

%I #18 Aug 16 2019 00:45:40

%S 2,2,31,4603,910307,352367441,23908162969,483148266971

%N a(n) is the least prime such that each concatenation of 1 <= k <= n consecutive primes beginning with a(n) is prime, or 0 if no such prime exists.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_708.htm">Puzzle 708 Find sets of k consecutive primes such that ...</a>, The Prime Puzzles & Problems Connection.

%e a(2)=2; 2, 3 are 2 consecutive primes and their concatenation 23 is also prime.

%e a(3)=31 since 31, 37, and 41 are 3 consecutive primes and 3137 and 313741 are both prime.

%t a[n_] := Block[{p = Prime@ Range@ n}, While[! AllTrue[Range[2, n], PrimeQ@ FromDigits@ Flatten@ IntegerDigits@ Take[p, #] &], p = Append[ Rest@ p, NextPrime@ Last@ p]]; p[[1]]]; Array[a, 5] (* _Giovanni Resta_, Jul 16 2019 *)

%Y Cf. A030996.

%K nonn,base,more

%O 1,1

%A _Jean-Marc Rebert_, Jul 16 2019

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)