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
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
Programs
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PARI
T(n,k)=my(p=prime(k+1),s); forstep(i=n%p, n-1, p, s+=valuation(n-i, p)<
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).
Comments