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

0,4

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.

Links

Table of n, a(n) for n=0..69.

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).

Example

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.

Prog

(PARI) T(n, k)=my(p=prime(k+1), s); forstep(i=n%p, n-1, p, s+=valuation(n-i, p)<<i); s
for(n=1, 20, for(k=1, max(primepi(n)-1, 1), print1(T(n, k)", ")); print) \\ Charles R Greathouse IV, Mar 12 2014

Crossrefs

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

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

Sequence in context: A352544 A363596 A354280 * A057560 A085592 A174421

Adjacent sequences: A239145 A239146 A239147 * A239149 A239150 A239151

Keyword

nonn,easy,tabf

Author

Bob Selcoe, Mar 11 2014

Status

approved