cp's OEIS Frontend

A025127 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A023533, t = A000040 (primes).

%I A025127 #6 Sep 14 2022 20:41:18
%S A025127 3,5,7,11,13,17,30,36,46,50,60,70,74,84,94,102,108,120,161,171,187,
%T A025127 197,209,229,243,253,271,281,289,313,323,339,363,381,391,403,421,431,
%U A025127 530,552,568,592,618,630,650,674,696,712,746,768,794,802,830,846,872,906,922,942,962
%N A025127 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A023533, t = A000040 (primes).
%H A025127 G. C. Greubel, <a href="/A025127/b025127.txt">Table of n, a(n) for n = 1..5000</a>
%t A025127 b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
%t A025127 A025127[n_]:= A025127[n]= Sum[b[n-j+2]*Prime[j], {j, Floor[(n+4)/2], n+1}];
%t A025127 Table[A025127[n], {n,100}] (* _G. C. Greubel_, Sep 14 2022 *)
%o A025127 (Magma)
%o A025127 A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
%o A025127 A025127:= func< n | (&+[NthPrime(n+2-k)*A023533(k): k in [1..Floor((n+1)/2)]]) >;
%o A025127 [A025127(n): n in [1..100]]; // _G. C. Greubel_, Sep 14 2022
%o A025127 (SageMath)
%o A025127 def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..13))
%o A025127 @CachedFunction
%o A025127 def A025127(n): return sum(b(n-j+2)*nth_prime(j) for j in (((n+4)//2)..n+1))
%o A025127 [A025127(n) for n in (1..100)] # _G. C. Greubel_, Sep 14 2022
%Y A025127 Cf. A000040, A023533.
%K A025127 nonn
%O A025127 1,1
%A A025127 _Clark Kimberling_