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- Interesting property identified for the pair of sequences A207324 and A030298:
- Since both sequences are based on particular ways of reading permutations, we may
- expect to find similarities among its terms.
- The first 105 terms for A207324 are (without commas):
- 112211231323123212312131234124314234123413214321342132431243142341243124321342132413214231423412431423142
- The same quantity of terms found for A030298 when visited (at least on Sat, Sept 15th 2012 at 19:04 VET) are:
- 112211231322132313123211234124313241342142314322134214323142341241324313124314232143241341234214123413242
- Placing these rows closer and comparing:
- 112211231323123212312131234124314234123413214321342132431243142341243124321342132413214231423412431423142
- 112211231322132313123211234124313241342142314322134214323142341241324313124314232143241341234214123413242
- We may compare the equality of corresponding columns by offset from left to right, finding a pattern:
- yyyyyyyyyyyyyyyyyNNNNNNyyyyyyyyyNNNNNNNNNNNyyyyNNNNNNNNNNNyNNyNNyyNNNNNNNyNyNNNyyNNyyNNNNyNNNNyNNNNyNyNyy
- 111111111111111110000001111111110000000000011110000000000010010011000000010100011001100001000010000101011
- Which may be called the answer pattern for the question: Are the columns values identical?, made 105 times,
- one time per column.
- But the equality isn't the unique question we may propose as criteria for building the pattern.
- Another interesting questions all of them of course matter of comparison, are:
- -Are both values (top and bottom) prime numbers?
- -Are both values (top and bottom) odd numbers?
- -Are both values (top and bottom) even numbers?
- -Are both values (top and bottom) perfect numbers?
- -Are both values (top and bottom) Mersenne numbers?
- -Are both values (top and bottom) Mersenne primes?
- -Does both values sum a prime number?
- -Are one of these values some integer power or exact root respect the other?
- -Have these values an integer (arithmetical) average?
- -Have these values an odd or even GCD?
- An extra conceptual dimen could be added if we consider as the value on a new sequence associated with a given offset
- the decimal number for the binary digits pattern built based on some kind of comparison where the offset consists
- of how many terms are picked and from each one A207324 and A030298 for comparison.
- Then, there is a lot of interesting sequences which one may think to build.
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