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).

3, 5, 7, 11, 13, 17, 30, 36, 46, 50, 60, 70, 74, 84, 94, 102, 108, 120, 161, 171, 187, 197, 209, 229, 243, 253, 271, 281, 289, 313, 323, 339, 363, 381, 391, 403, 421, 431, 530, 552, 568, 592, 618, 630, 650, 674, 696, 712, 746, 768, 794, 802, 830, 846, 872, 906, 922, 942, 962

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A023533.

Programs

Magma

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
A025127:= func< n | (&+[NthPrime(n+2-k)*A023533(k): k in [1..Floor((n+1)/2)]]) >;
[A025127(n): n in [1..100]]; // G. C. Greubel, Sep 14 2022

Mathematica

b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];
A025127[n_]:= A025127[n]= Sum[b[n-j+2]*Prime[j], {j, Floor[(n+4)/2], n+1}];
Table[A025127[n], {n,100}] (* G. C. Greubel, Sep 14 2022 *)

SageMath

def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..13))
@CachedFunction
def A025127(n): return sum(b(n-j+2)*nth_prime(j) for j in (((n+4)//2)..n+1))
[A025127(n) for n in (1..100)] # G. C. Greubel, Sep 14 2022