A144305 Triangle read by rows: prime numbers p(n) along left edge (n, 1) and totient phi(n) along right edge (n, n), with (n, k) = (n - 1, k - 1) + (n - 1, k) for 1 < k < n when n > 2.

1, 2, 1, 3, 3, 2, 5, 6, 5, 2, 7, 11, 11, 7, 4, 11, 18, 22, 18, 11, 2, 13, 29, 40, 40, 29, 13, 6, 17, 42, 69, 80, 69, 42, 19, 4, 19, 59, 111, 149, 149, 111, 61, 23, 6, 23, 78, 170, 260, 298, 260, 172, 84, 29, 4, 29, 101, 248, 430, 558, 558, 432, 256, 113, 33, 10

Offset

1,2

Comments

(1, 1) = 1 is considered a member of both sequences.

If (n, n - 1) is a prime p, n is less than or equal to the index of p (A049084(p) + 1) and strictly less if n >= 8: (8, 7) = 19 and (9, 1) = 19.

If (n, k) is a prime p, with n > 3 and 1 < k < n - 1, then n < A049084(p) + 1: (5, 2) = (5, 3) = 11 and (6, 1) = 11.

Excluding the right edge, the triangle has deteriorating symmetry about its midline until n = 12: (12, 5) = 988 and (12, 7) = 990.

The diamond of symmetry ends with (11, 5) = (11, 6) = 558 and coincidentally 11 is the last row which could be entered.

There is a related triangle which begins with p(1) = 2 and phi(1) = 1 on the first row, omitting the peak:

2 1

3 3 1

5 6 4 2

7 11 10 6 2

11 18 21 16 8 4

It appears to have less interesting properties.

Links

Table of n, a(n) for n=1..66.

Crossrefs

Cf. A000040, A000010

Sequence in context: A319254 A210864 A349550 * A138635 A128182 A059739

Adjacent sequences: A144302 A144303 A144304 * A144306 A144307 A144308

Keyword

easy,nonn,tabl

Author

Reikku Kulon, Sep 17 2008

Status

approved