A165401 Antidiagonally reading the array, formed via: first, writing the primes in the first row (row_1), and forming all successive rows' elements using the previous rows' elements as: row_2(j) = row_1(j)*row_1(j+1) - row_1(j) - row_1(j+1), and so on. The first 'column' of the array, 2 1 -1 -1 -1 -1 -1 -1 ... is converted to its absolute value.

2, 1, 3, 1, 7, 5, 1, 131, 23, 7, 1, 165619, 1275, 59, 11, 1, 1443643414307, 8716707, 6843, 119, 13, 1, 1930155333520916730618052608, 1337002832135523, 153383955, 22419, 191, 17, 1

Offset

1,1

Comments

The actual array that leads to the list given above is:

2 3 5 7 11 13 17 19 ...

1 7 23 59 119 191 287 395 ...

1 131 1275 6843 22419 54339 112683 241915 ...

1 165619 8716707 ...

1 1443643414307 ...

It can be observed that:

1) Obviously, all primes will appear in the list at least once, as the first row of the generating array is composed of all the primes.

2) There exist primes that appear more than once (e.g., 23, 59, 131, 191...).

3) When we have two successive primes in a row, prime(i) & prime(i+1) -as in all of the first row, and occasionally in other rows- the element just below these two is, obviously, Euler_tot( prime(i) * prime (i+1) ) - 1.

Links

Table of n, a(n) for n=1..29.

Crossrefs

Cf. A000040: The list of prime numbers is the first row of the array, that is converted to the list. Cf. A037165: This list, "Prime(n)*prime(n+1)-prime(n)-prime(n+1)" is the second row of the array, that is converted to the list.

Sequence in context: A129646 A277640 A370906 * A319916 A213074 A140966

Adjacent sequences: A165398 A165399 A165400 * A165402 A165403 A165404

Keyword

nonn,tabl

Author

Umut Uludag, Sep 17 2009

Status

approved