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A239148
Expansion of triangle T(n,k) of p-adic valuations of A052129(n) (Somos' quadratic recurrence sequence).
0
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.
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
KEYWORD
nonn,easy,tabf
AUTHOR
Bob Selcoe, Mar 11 2014
STATUS
approved