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

1,1

Links

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A000040, A023533.

Sequence in context: A239391 A087382 A355845 * A024883 A024328 A032529

Adjacent sequences: A025124 A025125 A025126 * A025128 A025129 A025130

Keyword

nonn

Author

Clark Kimberling

Status

approved