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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
2, 10, 14, 27, 53, 245, 293, 539, 9221 (list; graph; refs; listen; history; text; internal format)
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.
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.
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).
Cf. A217682.
Sequence in context: A160773 A217191 A190043 * A102340 A358749 A293931
James G. Merickel, Oct 10 2012
a(9) added by James G. Merickel, May 02 2013

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Last modified June 22 09:21 EDT 2024. Contains 373568 sequences. (Running on oeis4.)