A239148 Expansion of triangle T(n,k) of p-adic valuations of A052129(n) (Somos' quadratic recurrence sequence).

0, 0, 1, 2, 1, 6, 2, 12, 4, 1, 25, 9, 2, 50, 18, 4, 1, 103, 36, 8, 2, 206, 74, 16, 4, 413, 148, 33, 8, 826, 296, 66, 16, 1, 1654, 593, 132, 2, 3308, 1186, 264, 64, 4, 1, 6617, 2372, 528, 129, 8, 2, 13234, 4745, 1057, 258, 16, 4, 26472, 9490, 211, 516, 32, 8, 52944, 18980, 4228, 1032, 64, 16, 1, 105889

Offset: 0

Author

Bob Selcoe, Mar 11 2014

Keywords

• nonn
• easy
• tabf

Comments

Sum of triangle rows => A238496(n).

Only repeated values are powers of 2; all others are non-repeating.

When n=2p (p>2): T(n,k)=2^p+1.

Examples

			2    3    5    7    11   13...  (p)
0
0
1
2    1
6    2
12   4    1
25   9    2
50   18   4    1
103  36   8    2
206  74   16   4
413  148  33   8
826  296  66   16   1
1654 593  132  32   2
3308 1186 264  64   4    1
6617 2372 528  129  8    2
T(11,2)=66 because the (k+1)-th (3rd) prime is 5, and the 5-adic valuation of A052129(11)=66,
T(14,3)=129=2^7+1; n=2p because the (k+1)-th (4th) prime is 7.
		

Crossrefs

Cf. A052129, A238496, A238462 (2-adic valuation of A052129).

Cf. A001045 (Jacobsthal numbers - see A052129 for relationship with this sequence).

Programs

PARI

T(n,k)=my(p=prime(k+1),s); forstep(i=n%p, n-1, p, s+=valuation(n-i, p)<Charles R Greathouse IV, Mar 12 2014

Formula

T(n,k) = p-adic valuations of n*A052129(n-1)^2 (n>1; p=>(k+1)-th prime).

When k is constant and P' means "p-adic valuations of": P'a(n) = 2*P'a(n-1) + P'(n).