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A217681 a(n) produces only composites by concatenating numbers decremented in sequence in all bases from 2 up to a record. 3

%I

%S 2,10,14,27,53,245,293,539,9221

%N a(n) produces only composites by concatenating numbers decremented in sequence in all bases from 2 up to a record.

%C A217682(n) gives the value of the first arithmetic base in which any prime may be found leading with A217681(n) and proceeding by the concatenation of numbers decreasing in sequence. The simplest example of the kind of prime that needs to be found is 43, but of course we see from this sequence that in binary there is a prime in the set {10011, 1001110, 10011101} (The sequence does not consider the improper 'concatenation' of just the stem value alone), so our decimal 43 never is considered.

%C a(9)=9221 required 2-to-3 month-windows using a 32-bit version of PARI/GP (incl. the ispseudoprime() function -- not isprime() -- a powerful PROBABLE prime test) to verify.

%e Binary has a prime of the kind sought for every stem value 2-9, but every value in {10101001, 101010011000, 101010011000111, 101010011000111110, 101010011000111110101, 101010011000111110101100, 1010100110011111010110011, 1010100110001111101011001110, 10101001100011111010110011101} in binary is composite, so that 10 is this sequence's second term (and the companion sequence tells in what base a prime is first found).

%Y Cf. A217682.

%K nonn,base,less

%O 1,1

%A _James G. Merickel_, Oct 10 2012

%E a(9) added by _James G. Merickel_, May 02 2013

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)