[seqfan] sequence based on A050873 triangular array for GCD(u,v)
Jamie Morken
jmorken at shaw.ca
Mon Jul 31 17:57:59 CEST 2017
Hi,For the sequence A050873, I'd like to propose a sequence based on it,
but am not sure what the formula for the sequence is, and need help tofind some more terms.Here is the sequence so far:n a(n)1 12 23 64 125 306 607 2108 8409 61210 42011 2310For prime n, a(n) is a Primorial number.Example of how to construct the sequence from A050873, for n = 3Use the first 3 columns of A050873 starting at row 3 and identify the count of consecutive rows until a repeating pattern occurs.1 1 31 2 11 1 11 2 31 1 11 2 1The first three columns of A050873 starting at the third row is a repetition of those 6 rows, so the next row is 1 1 3.Example for n = 11Use the first 11 columns of A050873 starting at row 11:1 1 1 1 1 1 1 1 1 1 111 2 3 4 1 6 1 4 3 2 11 1 1 1 1 1 1 1 1 1 11 2 1 2 1 2 7 2 1 2 1...It takes 2310+1 rows before the patterns shows up and then the first eleven columns startingat the eleventh row is a repetition of those 2310 rows.The prime rows have a Pn row count for the repetition, but calculating the non prime column row counts like above seems harder, I don't know if there is a formula for it like for the primecolumns row counts, but maybe someone can find it or could calculate more values of thesequence. Thanks.cheers,Jamie
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